1. Slope-intercept Form y = mx + b

2. In order to identify the slope and y-intercept, you have to make sure that the problem is in slope- intercept form. This means that y has been solved for.

3. Examples y = 4x + 3 y = 4x + 3 Looking at the problem, we see that it starts off with y =. On the other side is our x variable and then our constant term (a term without a variable, just a number). Therefore, our problem is in slope-intercept form. Looking at the problem, we see that it starts off with y =. On the other side is our x variable and then our constant term (a term without a variable, just a number). Therefore, our problem is in slope-intercept form. Our slope is only the number in front of x, which is 4 and our y-intercept is 3. Our slope is only the number in front of x, which is 4 and our y-intercept is 3.

4. Examples Cont. y + 7 = x y + 7 = x Just by looking at the problem, it reads y + 7, so it lets us know that it is not in the correct form. At this point, we need to put it in slope-intercept form by solving for y. Just by looking at the problem, it reads y + 7, so it lets us know that it is not in the correct form. At this point, we need to put it in slope-intercept form by solving for y. Next to y is 7, so to get rid of this subtract 7 from both sides and we get y = x – 7. This is in slope-intercept form. There is an understood 1 in front of the x so our slope is 1. Our y-intercept is -7. Next to y is 7, so to get rid of this subtract 7 from both sides and we get y = x – 7. This is in slope-intercept form. There is an understood 1 in front of the x so our slope is 1. Our y-intercept is -7.

5. Examples Cont. 3x – 5y = 30 3x – 5y = 30 Our x and y are on the same side so this lets us know that this is not in slope-intercept form. Our x and y are on the same side so this lets us know that this is not in slope-intercept form. Because it is not in slope-intercept form, we CANNOT state what the slope and y-intercept are. Because it is not in slope-intercept form, we CANNOT state what the slope and y-intercept are. Let’s now begin to solve for y. Let’s now begin to solve for y.

6. Examples Cont. 3x – 5y = 30 3x – 5y = 30 -3x -3x Subtract 3x from both sides. -3x -3x Subtract 3x from both sides. -5y = -3x + 30 -5y = -3x + 30 Now we need to solve for y. To do so, divide EVERYTHING by what is in front of y. Here, it is -5. Now we need to solve for y. To do so, divide EVERYTHING by what is in front of y. Here, it is -5. -5y = -3x + 30 -5y = -3x + 30 -5 -5 -5 -5 -5 -5

7. Examples Cont. -5y = -3x + 30 -5y = -3x + 30 -5 -5 -5 -5 -5 -5 Now simplify. Now simplify. y = 3/5x – 6 y = 3/5x – 6 Our slope is 3/5 and our y-intercept is -6. Our slope is 3/5 and our y-intercept is -6.

8. Independent Practice Put the following problem in slope- intercept form. Put the following problem in slope- intercept form. What is the slope and y-intercept? What is the slope and y-intercept? -6x – 7y = 28 -6x – 7y = 28

9. Independent Practice Cont. -6x – 7y = 28 -6x – 7y = 28 +6x +6x Add 6x to both sides. +6x +6x Add 6x to both sides. -7y = 6x + 28 -7y = 6x + 28 -7 -7 -7 Divide everything by -7 -7 -7 -7 Divide everything by -7 Simplify. Simplify. y = -6/7x – 4 Our slope is -6/7 and our y-intercept is - 4.

10. Reminders You can only state what the slope and y-intercept are when the equation is in slope-intercept form. Don’t guess at it. You can only state what the slope and y-intercept are when the equation is in slope-intercept form. Don’t guess at it. When solving for y, divide everything by what is in front of y. When solving for y, divide everything by what is in front of y.