Slope-intercept FormSlope-intercept Form

y = mx + by = mx + b

In order to identify the In order to identify the slope and y-intercept, you slope and y-intercept, you

have to make sure that have to make sure that the problem is in slope-the problem is in slope-

intercept form. This intercept form. This means that y has been means that y has been

solved for.solved for.

ExamplesExamples y = 4x + 3y = 4x + 3 Looking at the problem, we see that it Looking at the problem, we see that it

starts off with y =. On the other side starts off with y =. On the other side is our x variable and then our constant is our x variable and then our constant term (a term without a variable, just a term (a term without a variable, just a number). Therefore, our problem is in number). Therefore, our problem is in slope-intercept form.slope-intercept form.

Our slope is only the number in front Our slope is only the number in front of x, which is 4 and our y-intercept is of x, which is 4 and our y-intercept is 3. 3.

Examples Cont.Examples Cont. y + 7 = xy + 7 = x Just by looking at the problem, it reads Just by looking at the problem, it reads

y + 7, so it lets us know that it is not in y + 7, so it lets us know that it is not in the correct form. At this point, we the correct form. At this point, we need to put it in slope-intercept form need to put it in slope-intercept form by solving for y.by solving for y.

Next to y is 7, so to get rid of this Next to y is 7, so to get rid of this subtract 7 from both sides and we get y subtract 7 from both sides and we get y = x – 7. This is in slope-intercept form. = x – 7. This is in slope-intercept form. There is an understood 1 in front of the There is an understood 1 in front of the x so our slope is 1. Our y-intercept is -x so our slope is 1. Our y-intercept is -7. 7.

Examples Cont.Examples Cont. 3x – 5y = 303x – 5y = 30 Our x and y are on the same side Our x and y are on the same side

so this lets us know that this is so this lets us know that this is not in slope-intercept form.not in slope-intercept form.

Because it is not in slope-intercept Because it is not in slope-intercept form, we CANNOT state what the form, we CANNOT state what the slope and y-intercept are.slope and y-intercept are.

Let’s now begin to solve for y.Let’s now begin to solve for y.

Examples Cont.Examples Cont. 3x – 5y = 30 3x – 5y = 30 -3x -3x Subtract 3x from both -3x -3x Subtract 3x from both

sides.sides. -5y = -3x + 30 -5y = -3x + 30 Now we need to solve for y. To do so, Now we need to solve for y. To do so,

divide EVERYTHING by what is in front divide EVERYTHING by what is in front of y. Here, it is -5.of y. Here, it is -5.

-5y-5y = = -3x-3x + + 3030

-5 -5 -5-5 -5 -5

Examples Cont.Examples Cont. -5y-5y = = -3x-3x + + 3030

-5 -5 -5-5 -5 -5

Now simplify.Now simplify.

y = 3/5x – 6y = 3/5x – 6

Our slope is 3/5 and our y-intercept Our slope is 3/5 and our y-intercept is -6.is -6.

Independent PracticeIndependent Practice Put the following problem in Put the following problem in

slope-intercept form.slope-intercept form.

What is the slope and y-What is the slope and y-intercept?intercept?

-6x – 7y = 28-6x – 7y = 28

Independent Practice Cont.Independent Practice Cont. -6x – 7y = 28-6x – 7y = 28 +6x +6x Add 6x to both sides.+6x +6x Add 6x to both sides. -7y-7y = = 6x6x + + 2828

-7 -7 -7 Divide everything by -7-7 -7 -7 Divide everything by -7

Simplify.Simplify.

y = -6/7x – 4 y = -6/7x – 4

Our slope is -6/7 and our y-intercept is - Our slope is -6/7 and our y-intercept is - 4.4.

RemindersReminders You can only state what the You can only state what the

slope and y-intercept are when slope and y-intercept are when the equation is in slope-intercept the equation is in slope-intercept form. Don’t guess at it.form. Don’t guess at it.

When solving for y, divide When solving for y, divide everything by what is in front of everything by what is in front of y.y.