Slope Intercept Form & Graphing

By: Schelbi, Logan, Brendan, and Shay

What is Slope-Intercept Form

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. Linear equations can have one or more variables. Linear equations occur with great regularity in applied mathematics. The form y=mx+b... y is the total or what your finding, m is your slope, x is your variable, and b is your y int.

Example of Slop Intercept #1

Our first example is y-3/4x=0. We need to get y by itself, so our first step will be to add 3/4x to both sides. That cancels out the 3/4x on the left side, so you get y=0+3/4x. Now, since you don’t need the 0, let’s just get rid of it. Your final answer is y=3/4x.

Example of Slope Intercept Form #2

Our next example is 2x+4y=8. Since we want to get y by itself, you must start by subtracting 2x to both sides. You will end up with 4y=8-2x since subtracting 2x to the left side cancelled it out. We aren’t done yet. We still need just y, not 4y. So you simply need to divide both sides by 4. You will then end up with y=8-2x/4. In other words, you get y=2-.5x. Your last step will be to get the slope (x) first, and the constant (a number with no variable) last. Your final answer is y=-1/2x+2

How to Graph and write a table for an equation

Example #1: Y=3/4x

Example #2: Y=-1/2x+2

1. For this table, when x is 0, y is 0. If you need proof, you simply substitute x with 0 again and solve it. Next, substitute x with 1,2,3, etc, again until you find a pattern.

When you graph it, you need to plot (0,0) first because that's where the line will cross the y axis. This one will be a positive slope because there is not a negative sign in front of the slope. Then each point after that will be 3 squares up and 4 squares over. (rise: 3 and run: 4)

2. Making a table and graph with a slope intercept equation is very simple. To create the table, you first need to substitute x with 0 to find the y-intercept. Since the constant number is 2, we already know our y-intercept so, in the table, when x is 0, y is 2. From there on, just substitute x for 1,2,3, etc. and solve until you find a pattern.

Now onto graphing. Your first plot point will be (0,2) because that's the y-intercept. Don't forget it's a negative slope (the sign in front of mx is what tells you if it's negative or positive) From there on, your next points will be 1 rise, and 2 run from your next one (one square down, two squares over).

Now its your turn to solve (Word Problems for y-intercept...)

1. Charlie is going to an indoor skiing facility. The equipment alone cost 45 dollars. Skiing cost 25 dollars per hour. Write an equation in y-intercept form to figure out how much they’re going to pay after x amount of hours.

2. Sara is going to Johnson & Adams Amusement Park. It cost 25 dollars to get into the amusement park, and 10 dollars per ride. Write an equation in y-intercept form to figure out their total amount money spent after x amount of rides.

Answers to word problems

1. First you start the equation with the y-intercept. Anytime there is a down payment that will be the y-intercept. This down payment is $45. Now the slope is any amount of time or additional payment that continues to gradually increase. In this case it would be the 25 dollars per hour. So you would right that as 25x, and x being any amount of hours. To make the equation complete, you have to add the y= at the beginning. When you put all of these pieces together you get y=25x+45.

2. To put this problem into y-intercept form you should start with the y-intercept and work backwards. The y-intercept will always be the starting or down payment fee. In this case it’s the 25 dollar ticket. Then you have to get the slope which will be the amount of money depending on each ride. Each ride is 10 dollars so they have to pay 10 dollars each time making that the slope. Writing that will look like 10x. Then to make the equation y-intercept form you have to add y= to the beginning having the equation end up looking like y=10x+25.