3-6 Lines in the Coordinate Plane
Slope-intercept formula
y = mx + b
m and b are numbers. y and x will stay letters.
m is the slope,
b is the y-intercept. This is where the line crosses the y-axis
3
y x 2
5
Ex:
3
m
b  2
5
Given m = 4 b = 8, put in slope-intercept form y = 4x + 8
Point-slope formula—used when you know the slope and a point on the line or two points.
Solving for y in point-slope formula puts the equation in slope-intercept form.
y and x remain letters. y1, x1, and m are letters. m is the slope. x1 and y1 are point’s
coordinates (x1, y1)
Example Given m = 2 and (3, -4) put in slope intercept form
y – (-4) = 2 (x - 3). Now “clean up” the double negative
y + 4 = 2 (x -3)
To put in slope-intercept form: Distribute the 2
y+ 4 = 2x -6
y = 2x -10
Example: Given two points, give the equation of the line in slope intercept form.
(6, -4) ( 8, 2)
First, find the slope 2 – (-4) = 2+4 = 6 = 3
8 -6
2
2
Next, pick one of the points and use point-slope formula. You will get the same answer for
either point. If a point has a 0 in it, pick it—this is less work.
y – 2 = 3(x -8)
y – 2 = 3x -24
y = 3x – 22
y – (-4) = 3 (x – 6)
y + 4 = 3x - 18
y = 3x - 22