## How to Graph Equation of a Line, y=mx+b: Algebra

Hi everyone, welcome back to Mathsux! This week we’ll be reviewing how to graph an equation of a line in y=mx+b form. And if you have not checked out the video below, please do! Happy calculating! 🙂

An equation of a line can be represented by the following formula:

y=mx+b

Y-Intercept: This is represented by b, the stand-alone number in y=mx+b. This represents where the line hits the y-axis.  This is always the first point you want to start with when graphing at coordinate point (0,b).

Slope: This is represented by m, the number next to x in y=mx+b. Slope tells us how much we go up or down the y-axis and left or right on the x- axis in fraction form:

Now let’s check out an Example!

Graph the following:

-> First, let’s identify the slope and y-intercept of our line.

-> To start, let’s graph the first point on our graph, the y-intercept at point (0,1):

-> Now for the slope. We are going to go up one and over to the right one for each point, since our slope is 1/1.

-> Connect all of our coordinate points and label our graph.

Try the following practice questions on your own!

Practice Questions:

Want more Mathsux?  Don’t forget to check out our Youtube channel and more below! And if you have any questions, please don’t hesitate to comment below. Happy Calculating! 🙂

Need to brush up on slope? Click here to see how to find the rate of change.

## 4 Ways to Factor Trinomials: Algebra

Greeting math peeps and welcome to MathSux! In this post, we are going to go over 4 ways to Factor Trinomials and get the same answer, including, (1) Quadratic Formula (2) Product/Sum, (3) Completing the Square, and (4) Graphing on a Calculator.  If you’re looking for more don’t forget to check out the video and practice questions below.  Happy Calculating! 🙂

Also, if need a review on Factor by Grouping or Difference of Two Squares (DOTS) check out the hyperlinks here!

*If you haven’t done so, check out the video that goes over this exact problem, and don’t forget to subscribe!

We will take this step by step, showing 4 ways to factor trinomials, getting the same answer each and every time! Let’s get to it!

## (1) Quadratic Formula:

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## (2) Product/Sum:

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## (3) Completing the Square:

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## (4) Graph:

Choose the factoring method that works best for you and try the practice problems on your own below!

Practice Questions:

Solutions:

Want a review of all the different factoring methods out there?  Check out the ones left out here (DOTS and GCF) and happy calculating! 🙂

For even more ways to factor quadratic equations, check out How to factor by Grouping here! 🙂

Also, if you want more Mathsux?  Don’t forget to check out our Youtube channel and more below! If you have any questions, please don’t hesitate to comment below. Happy Calculating! 🙂

## Completing the Square: Algebra

Want to learn the ins and out of completing the square?  Then you’ve come to the right place! Learn how to Complete the Square step by step in the video and article below, then try the practice problems at the end of this post to truly master the topic! If you’re looking for more on completing the square, check out this post here. Happy Calculating! 🙂 Check out the video below for an in-depth look at completing the square:
To answer this question, there are several steps we must follow including: Step 1: Move the whole number, which in this case is 16, to the other side of the equation. Step 2: Make space for our new number on both sides of the equation.  This number is going to be found by using a particular formula shown below: Step 3: Add the number 9 to both sides of the equation, which we found using our formula. Step 4: Combine like terms on the right side of the equation, adding 16+9 to get 25. Step 5: Now, we need to re-write the left side of the equation using the following formula. Step 6: Finally, we solve for x by taking the positive and negative square root to get the following answer and solve for two different equations: Practice Questions: Solutions:

Want more Mathsux?  Don’t forget to check out our Youtube channel and more below! And if you have any questions, please don’t hesitate to comment below. Happy Calculating! 🙂

Need more of an explanation?  Check out why we complete the square in the first place here ! 🙂

## Rate of Change: Algebra

The rate of change, the rate of motion, the rate of a heartbeat. A chart on a piece of paper as boring as it may seem, can produce some pretty great numbers that directly relate to us human folk.

The question below may make you groan at first glance, but what happens if we use our imagination to picture the real-life bird it’s describing? Any better? Yes? No? Well, either way we must solve, so let’s get to it

## How do I answer this question?

It wants us to find the Rate of Change, specifically between 3 and 9 seconds. Let’s hi-light those two values on our given table:

## What is the Rate of Change?

To get the Rate of Change between these two values, we need to go back to the good ole’ Slope Formula and realize that the list of values is really a list of x and y coordinates.

Now let’s plug in the coordinate values (3, 6.26) and (9,3.41) into our slope formula:

Extra Tip! Notice that we added the labels feet/second to our answer.  Why does this make sense?? The question tells us that P(t) represents feet and that t is equal to seconds.  Another way to look at this question when applying it to the slope formula is to realize that we are finding the change of feet divided by the change of seconds.                                                          ____________________________________________________________________________________

Still got questions?  Let me know in the comments and as always happy calculating!:)

Looking for the next step? Learn how to graph equation of a line, y=mx+b here!

## How to Factor Quadratic Equations: Algebra

In this post, we are going to dive deep into how to factor Quadratic equations! There are so many different methods to choose from including GCF, Product/Sum, DOTS, and the Quadratic Formula.  Here we will go step by step into each method on how to factor quadratic equations, each with their own set of practice questions. For a review on how to factor by grouping, check out this post here and  happy calculating! 🙂

Why factor in the first place, you may say? We want to manipulate the equation until we solve for x.  Solving for x is our main goal, and factoring allows us to do that.  Now let’s get to the good stuff!

## Greatest Common Factor (GCF):

The greatest common factor is the highest possible number that can be divided out from an equation.  This gets the equation into its simplest form and makes it easier for us to solve for x.

Before considering which type of factoring methdo to use, always ask yourself, “Can I take out a GCF?”

## Product/Sum:

This factoring method is for quadratic equations only! That means the equation takes on the following form:

## Difference of Two Squares DOTS)

Not to play favorites or anything, but DOTS is the easiest and most lovable of the factoring methods.  This factoring method just makes you feel all warm and fuzzy inside or maybe that’s just me).  Before we get into how to do DOTS, let’s talk about when?

## Quadratic Formula:

We have heard of the quadratic equations, so how id the quadratic formula different?

The Answer: The Quadratic Formula is what we use to factor any trinomial. You can use product/sum on trinomials like we discussed earlier, but this may not always work out easy.  The Quadratic Formila on the other hand will work every time!

Low and behold, the Quadratic Formula:

Want more Mathsux?  Don’t forget to check out our Youtube channel and more below! And if you have any questions, please don’t hesitate to comment below. Happy Calculating! 🙂

## Why Must We Complete the Square?: Algebra

Completing the Square: So many steps, such little time.  It sounds like it involves a square or maybe this is a geometry problem?  Why am I doing this again?  Why must we complete the square in the first place?

These are all the thoughts that cross our minds when first learning how to complete the square.  Well, I’m here to tell you there is a reason for all those steps and they aren’t that bad if you really break them down, let’s take a look!

Answer: x={-7,3}

Explanation:

I’m not going to lie to you here, there are a lot of seemingly meaningless steps to completing the square.  The truth is though (as shocking as it may be), is that they are not meaningless, they do form a pattern, and that there is a reason! Before we dive into why let’s look at how to solve this step by step:

Feeling accomplished yet!? Confused?  All normal feelings.  There are many steps to this process so go back and review, practice, and pay close attention to where things get fuzzy.

But the big question is why are we doing these steps in the first place?  Why does this work out, to begin with?

For those of you who are curious, continue to read below!

Want more Mathsux?  Don’t forget to check out our Youtube channel and more below! And if you have any questions, please don’t hesitate to comment below. Happy Calculating!

Need more of an explanation?  Check out why we complete the square in the first place here !

## PieceWise Functions NYS Regents: Algebra

Greetings math friends, students, and teachers I come in peace to review this piecewise functions NYS Regents question.  Are they pieces of functions? Yes. Are they wise?  Ah, yeah sure, why not? Let’s check out this piecewise functions NYS Regents question below and happy calculating! 🙂

1 value satisfies the equation because there is only one point on the graph where f(x) and g(x) meet.

Does the above madness make sense to you? Great!

Need more of an explanation? Keep going! There is a way to understand the above mess.

How do I read this?

Looking at this piece-wise function: We want to graph the function 2x+1 but only when the x-values are less than or equal to negative 1.

We also want to graph 2-x^2 but only when x is greater than the negative one.

One way to organize graphing each piece of a piecewise function is by making a chart.

1. Lets start by making a chart for the first part of our function 2x+1:

Is it all coming back to you now?  Need more practice on piece-wise functions?Check out this link here and happy calculating! 🙂

Also, if you’re looking to nourish your mind or you know, procrastinate a bit check out and follow MathSux on these websites!

## Factor by Grouping: Algebra 2/Trig.

Hey math friends! In this post, we are going to go over Factor by Grouping, one of the many methods for factoring a quadratic equation.  There are so many methods to factor quadratic equations, but this is a great choice, for when a is greater than 1. Also, if you need to review different types of factoring methods, just check out this link here.  Stay curious and happy calculating! 🙂 Before we go any further, let’s just take a quick look at what a quadratic equation is: Usually, we can just find the products, the sum, re-write the equation, solve for x, and be on our merry way.  But if you notice, there is something special about the question below. The coefficient “a” is greater than 1/. This is where factor by grouping comes in handy! Now that we know why and when we need to factor by grouping lets take a look at our Example:

Factor By Grouping: Hard to solve? No.  Hard to remember? It can be, just remember to practice, practice practice! Also, if you are in need of a review of other methods of factoring quadratic equations, click this link here.

Want more Mathsux?  Don’t forget to check out our Youtube channel and more below! And if you have any questions, please don’t hesitate to comment. Happy Calculating! 🙂

## Recursive Formula: Algebra

Howdy math peeps! In this post, we are going to go over the recursive formula step by step by reviewing an old Regent’s question. These things may look weird, confusing, and like a “what am I doing?” moment, but trust me they are not so bad! We are going to take a look at the Regents question below and then find the correct recursive formula that follows the given sequence by going through each answer choice. Before we begin to answer our questions though, we will first define and break down what a recursive sequence is. Also, be sure to check out the video at the end of this post for more examples and further explanation. Happy calculating!

Before we dive into the solution to this question, let’s first look at a recursive formula example and define what they are in the first place!

## What is the Recursive Formula?

A Recursive Formula is a formula that forms a sequence based on the previous term value. All this means is that it uses a formula to form a sequence-based pattern. Recursive formulas can take the shape of different types of sequences, including arithmetic sequences (sequence based on adding/subtracting numbers) or geometric sequences (sequence based on multiplying/dividing numbers). Check out the example below:

a1=2 , an+1=an+4

## How do You Solve a Recursive Equation?

When solving a recursive equation, we are always given the first term and a formula. We start by using the first given term of our sequence, usually represented as a1, and plug it into the given formula to find the value of the second term of the sequence. Then we take the value of the previous term (the second term in our sequence) and plug it into our formula again, to find the third value of our sequence…. and the pattern continues! The solutions we get from each step up forms a sequence. If this sounds confusing, don’t worry because we are going to look at an example! Take a look at the recursive formula below:

a1=2 , an+1=an+4

Now let’s take another look at our recursive formula, this time breaking down what each part means:

a1 always represents the first given term, which in this case is a1=2. Next, we plug in 2 for an into our formula an+4 to get (2)+4=6. This gives us our second term in the sequence, which is 6. Next, we plug in 6 into the formula to get (6)+4=10, which is the value of the third term in the sequence. And we continue the pattern, always taking the value of the preceding term! In this case, I just found the first few terms below, but the recursive formula can continue infinitely! Again , if this sounds confusing, please take look at the pattern below:

Terms of the Sequence: 2, 6, 10, 14, 18….

Notice all the terms of the sequence are circled in pink, forming a sequence of, 2, 6, 10, 14, 18!? This is what the recursive formula produces!

## Now back to our Original Question:

Q: What recursively-defined function represents the sequence 3, 7, 15, 31,

(1) f(1) = 3, f(n + 1) = 28 (n) +3

(2) f(1) = 3, f (m + 1) = 28(0) – 1

(3) f(1) = 3, f(n + 1) = 28 (n) +1

(4) f(1) = 3, f (n + 1) = 38 (n) -2

How do I answer this question?

At first glance, all of these answer choices may look exactly the same as there are many recursive formulas to choose from. The first thing we need to do is to identify how each answer choice is different. Notice below, the section highlighted in green? This is what we will focus on for finding the correct recursive formula!

The question we are working with actually gives us a sequence and we need to find the recursive formula that works with it! Our goal with this question is to work backward to test out each recursive formula given to us until we get the correct sequence. To begin, let’s first identify each term in our given sequence.

As we go through each answer choice, we are looking for the recursive formula that gives us the above sequence 3, 7, 15, 31. Let’s start with choice (1) which happens to be a type of geometric sequence.

Right away we can see the sequence forming for choice (1) is 3, 11, … where the first term, 3, matches our original sequence, but the second term we get which is, 11, does not. This means we will need to move on and find the sequence of the next option, choice (2), which happens to be another type of geometric sequence. Let’s take a look:

For choice (2), we can see that the sequence we get is 3, 7, 127 which matches our given sequence for the first two terms 3, 7, but does not match the third term 127, when we need a 15 here (the original sequence is 3,7,15,31). Thus, we must move onward to the next recursive formula by testing out choice (3), which this time is an arithmetic sequence! Maybe we will have better luck!

This last option, choice (3) provided us with the same sequence we were originally provided within the original question, 3, 7, 15, 31. We have found our answer and now we can celebrate!

## Recursive Formula Examples

Still have questions about recursive formulas? Check out more on recursive formula examples here and in the video above! And if you’re looking to learn all there is to know about sequences, check out this post here! Looking to move ahead? Check out the infinite geometric series lesson here! Also, please don’t hesitate to comment with any questions. Happy calculating! 🙂