Student Note: 5.13: Finding the Equation of a Line Part #2 – Parallel and

Perpendicular Lines

Recall:

Parallel Lines Perpendicular Lines • Parallel lines are lines that do not intersect.

• The slopes of parallel lines are __________________________________________.

• The mathematical symbol for parallel lines is ______.

• Perpendicular lines are lines that intersect to form right angles.

• The slopes of parallel lines are __________________ ________________________.

• The mathematical symbol for parallel lines is ______.

Parallel Lines Practice Problems:

Example 1: What is the slope of a line that is parallel to the given line?

a) 𝑦 = −3

4𝑥 + 5 b) 4𝑥 + 𝑦 = 7 c) 7𝑥 − 2𝑦 = 3

Example 2: Write an equation of a line that is parallel to the given line and passes through the given point.

Given Line New Line

Example 3: Find the equation of a line that is parallel to 6𝑥 − 2𝑦 + 16 = 0 and passes through the point (−1, 2).

Perpendicular Lines Practice Problems:

Example 4: What is the slope of a line perpendicular to the given line?

a) 𝑦 = −2

3𝑥 − 5 b) 9𝑥 − 3𝑦 = −6 c) 5𝑥 + 7𝑦 = 4

Example 5: Write an equation of the line that is perpendicular to the given line and passes through the given point.

a) 𝑦 = −2

7𝑥 + 1 ; (−2, 3) b) 10𝑥 + 2𝑦 = −3 ; (0, −4)

Given Line: Given Line:

New Line: New Line:

Consolidation: 5.13: Finding the Equation of a Line Part #2 – Parallel and

Perpendicular Lines

For each of the following problems, find the equation of the line such that it satisfies the given information.

Perpendicular to the line 𝑦 =3

2𝑥 + 9 and goes through

(6, 1)

Goes through the point (2, −6) and is perpendicular to the line 2𝑥 − 𝑦 = 4.

The line has the same 𝑦-intercept as the line 𝑦 = −3𝑥 + 3, but is perpendicular to the line 2𝑥 + 4𝑦 + 15 = 0.

The line has the same 𝑥-intercept as the line 2𝑥 − 3𝑦 = 12, but is parallel to the line 3𝑥 − 𝑦 + 5 = 0.

The line has the same 𝑥-intercept and is perpendicular to the line 𝑦 = −𝑥 + 2.