Notes on Slope and Equations of Lines
𝑟𝑖𝑠𝑒
𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒
𝛥𝑦
𝑦 −𝑦
Slope (m) = 𝑟𝑢𝑛 = ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒 = 𝛥𝑥 = 𝑥2 −𝑥1
2
1
Y-intercept (b) = place where the line crosses the y-axis
Writing Equations of Lines
There are two forms that work well for writing equations of lines:

Slope/Intercept Form
y = mx + b

Point/Slope Form
y - y1 = m(x - x1)

The "red" values must be filled in to complete the equation
I. Write the equation of a line in SLOPE/INTERCEPT form.
Ex 1)
Given:
m=3
y-int = -2
Solution: y = 3x - 2
II. Write the equation of a line in POINT/SLOPE form. Then
change it to SLOPE/INTERCEPT form.
Ex 2)
Given:
m = -2
thru (-2, 5)
Solution: y - 5 = -2(x - 5)
y - 5 = -2x + 10
y
= -2x + 5
Ex 3)
Given:
(2, 3) and (1, 4)
Solution: Find slope
Choose 1 point
Write in point/slope
m = -1
(2, 3)
y - 3 = -1(x - 2)
y - 3 = -1x + 2
y
= -1x + 5
III. Write the equation of horizontal and vertical lines.
Ex 4)
Given:
A horizontal line through (-1, 7)
Solution: y = 7
Ex 5)
Given:
A vertical line through (11, 2)
Solution: x = 11
Ex 6)
Given:
A line parallel to the x-axis through (-4, -3)
Solution: y = -3
Ex 7)
Given:
A line perpendicular to x = 5 through (-5, -6)
Solution: y = -6
IV. Write the equation of lines from words.
Ex 8)
Given:
A line through (10, -2) and perpendicular to
y = -2x + 3
1
Solution: The slope is m = 2 and the point is (10, -2).
Use POINT/SLOPE form:
y -(-2) = (1/2)(x -10)
Change to SLOPE/INTERCEPT form:
y + 2 = (1/2)x - 5
y
= (1/2)x - 7