1. Writing Equations From Graphs
Slope-Intercept Form

2. Review
Any linear equation can be written in slope-intercept form by solving for y and simplifying. In this form, you can immediately see the slope and y-intercept. Also, you can quickly graph a line when the equation is written in slope-intercept form.

3. Review of Graphing from Slope-Intercept Form
Given the equation
y = 3x – 1
y = 3x – 1 is in the form y = mx + b
slope: m = 3 =
y-intercept: b = –1 •
Step 1 Plot (0, –1). •
Step 2 Count 3 units up and 1 unit right and plot another point.
Step 3 Draw the line connecting the two points.

4. Practice graphing from Slope-Intercept Form
Given the equation
y = -2x +3
y = -2x + 3 is in the form y = mx + b
slope: m =- 2 =
y-intercept: b = +3 • •
Step 1 Plot (0, 3).
Step 2 Count 2 units down and 1 unit right and plot another point.
Step 3 Draw the line connecting the two points.

5. Writing Equations from Graphs
Given the line
write an equation in slope-intercept form
Run = 3
Step 1 Find the y-intercept •
Rise = 4
This point is ( 0, -2) so the y-intercept is -2
Step 2 Move up or down the line until you reach another coordinate intersection. •
Step 3 Figure the rise and run from the y-intercept to the other point
A rise of 4 and a run of 3 gives us a slope of 4/3
Step 4 Write the equation of the line with a slope of 4/3 and y-intercept of -2 In slope-intercept form y = mx + b

6. Writing Equations from Graphs
Given the line
write an equation in slope-intercept form
Step 1 Find the y-intercept
Rise = -3 •
This point is ( 0, 2) so the y-intercept is + 2
Step 2 Move up or down the line until you reach another coordinate intersection. •
Run = 1
Step 3 Figure the rise and run from the y-intercept to the other point
A rise of -3 and a run of 1 gives us a slope of -3/1 or -3
Step 4 Write the equation of the line with a slope of -3 and y-intercept of +2

7. Now you try • • • • • • • • • • Y-int = -2 Slope = 6/-1 =-6 Y-int = 0
Slope = ½ or -1/-2 = ½ • • • •
Y-int = 0
Slope = 1/1 =1
Y-int = -2
Slope = 0/1 =0 • • • • •

8. Now you try • • • • • • • • 2. 1. Y-int = 0 Slope = 4/3 3. 4.
Y-int = none
Slope = undefined • • •

9. Now you try • • • • • • • • 6. 5. Y-int = 2 Slope = 4/3 8. 7.
Y-int = none
Slope = undefined • • •