4.6 Slope-Intercept Form

What are the two ways we know how to graph a

linear line so far?1.) Using a t-chart, and plotting points

2.) Using x and y intercepts

Let’s try graphing using a point and slope:

Point (2,3)

Slope = 2

Wouldn’t it be great if we could just look at an equation and figure out it’s slope and a point???!!!

WE CAN!!! YAHHHH!!!!

BY USING SLOPE-INTERCEPT FORM

SLOPE-INTERCEPT FORM

EXAMPLE #1

So all we have to do issolve for “y” and we can see a slope and a point!!!

Some more examples…

“b” is the y-intercept

So in order to use this form we must solve

for “y”+ 5X + 5X

3y = 5x + 9

3 3 3

-4x -4x

-y = -2x + 2

-1 -1 -1

Hand out two sheets of graph

paper to everyone!YOU NEED GRAPH PAPER FOR HW

FOLD UP INTO 6 BOXES ON EACH SIDE

1) Plot the y-intercept as a point on the y-axis. The constant, b = 1, so the y-intercept = 1.

2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 2, so the slope = 2/1.

up 2

right 1 up 2

right 1

m = 2/1b = (0, 1)

1) Plot the y-intercept as a point on the y-axis. The constant, b = -4, so the y-intercept = -4.

2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -1, so the slope = -1/1.

right 1down 1

right 1down 1

m = -1/1b = (0, -4)

1) Plot the y-intercept as a point on the y-axis. The constant, b = -2, so the y-intercept = -2.

2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 3/2, so the slope = 3/2.

right 2

up 3

right 2

up 3

m = 3/2b = (0, -2)

1) Plot the y-intercept as a point on the y-axis. The constant, b = 3, so the y-intercept = 3.

2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -2, so the slope = -2/1.

right 1down 2

right 1

down 2

YOU NEED TO SOLVE FOR “Y” FIRST!!

Let’s practice converting an equation to slope-intercept

form.In other words: SOLVE FOR “y”

1. 2x – y = -3 2. 4x + 2y = 6

3. -5x – 3y = 15 4. 4x + 3y = 24

-2x -2x -y = -2x – 3 y = 2x + 3

-4x -4x 2y = -4x + 6 y = -2x + 3

+5x +5x -3y = 5x + 15

-4x -4x 3y = -4x + 24

Now let’s look at each equation and decide what the slope and y-intercept is.

1. y = -3x + 6 2. y = 2x – 5

3. y = -x 4. 2y = 8x +10

5. x + 3y = 9 6. x – 2y = 16

m = b = (0,6) m = b = (0,-5)

m = b = (0,0)m = b = (0,5)

m = b = (0,3) m = b = (0,-8)

y = 4x + 5

y = mx + b