Equations of Lines

Overview

• Sections 3.5 & 8.1 in the textbook:
– Graphing Using the Slope and y -intercept
–Writing Equations using the Point -Slope
Formula
– Equations Using Two Points
– Equations of Horizontal and Vertical Lines
(8.1)
– Equations of Parallel and Perpendicular Lines
(8.1)

Graphing Using the Slope and
y -intercept

• Put the equation in slope- intercept form
– Recall slope- intercept form : y = mx + b

• Plot the y -intercept
(0, b)

• From the y-intercept, use the principle of
“rise over run” with the slope to generate
1 or 2 more points
– Need AT LEAST 2 points to make the line

Graphing Using the Slope and
y-intercept (Example)

Ex 1: Graph each line using the slope and
y-intercept:

a) y = -3x + 1
b) -2x + 3y = 6

Ex 2: Graph each line using the slope and
y-intercept:

a) y = x
b) -x – 2y = 4

Writing Equations Using the
Point- Slope Formula

Point-Slope Formula

• Point-Slope formula: y – y₁ = m(x – x₁)
– (x₁, y₁) is any point
– x and y are variables
– Very similar to the slope formula discussed in
section 3.4

• Along with slope-intercept form, DO NOT
forget about standard form:
Ax + By = C where A, B, and C are constants
• All variables on one side and the constants on the
other
• NO fractions

Point-Slope Formula (Example)

Ex 3: Write the equation of the line – leave the
answer in the requested form:

a) Slope of 3 and passes through (-2, 4) – leave
in slope-intercept form

b) Slope of -½ and passes through (6, 1) – leave
in slope-intercept form

c) Slope of 5 and passes through (0, -9) – leave in
standard form

Ex 4: Write the equation of the line – leave
the answer in the requested form:

a) Slope of -2 and passes through (5, -3)
– leave in standard form

b) Slope of ¼ and passes through (-8, -6)
– leave in slope-intercept form