The Equation of a Line

Slope – Intercept form: y = mx + b
◦ Use when you are given the slope and (0, b) or if
you are given the graph of the line.

Point-Slope form: y – y1 = m(x – x1)
◦ Use when you are given the slope and (x, y) or if
you are given 2 ordered pairs.
◦ Don’t leave your answer in the form, check the
directions to see what’s required.
1.
m = - ½ : (0, -4)
2.
m = 2; (4, -2)
3.
(-3,2) and (5, 7)
Note: A, B, and C are integers, and A > 0
To write an equation in this form:
1. Rearrange so that the x and y terms are on
the left and the constant is on the right.
2. If needed, multiply everything by the LCD to
clear any fractions.
3. If needed, multiply everything by -1 so the
coefficient of x is positive.

1. (1, 3) and (-2, -9)

2. (-5, -2) and (6, -4)


Parallel lines have equal slopes. Symbol: ||
Perpendicular lines have opposite reciprocal
slopes. Symbol: |
Ex: are the 2 lines ||, | , or neither?
6x – 2y = 7
x + 3y = -5
Write the equation of the line that passes
through the given point and is parallel to the
given equation: (-1, 1); y = -3x + 1
Write the equation of the line that passes
through the given point and is perpendicular
to the given equation: (2, 8); x + 2y = 9