Five-Minute Check (over Lesson 3–2)

CCSS

Then/Now

New Vocabulary

Key Concept: Slope of a Line

Example 1: Find the Slope of a Line

Concept Summary: Classifying Slopes

Example 2: Real-World Example: Use Slope as Rate of Change

Postulates: Parallel and Perpendicular Lines

Example 3: Determine Line Relationships

Example 4: Use Slope to Graph a Line

Content Standards

G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Mathematical Practices

4 Model with mathematics.

7 Look for and make use of structure.

8 Look for and express regularity in repeated reasoning.

You used the properties of parallel lines to determine congruent angles.

• Find slopes of lines.

• Use slope to identify parallel and perpendicular lines.

• slope

• rate of change

Find the Slope of a Line

A. Find the slope of the line.

Substitute (–3, 7) for (x1, y1) and (–1, –1) for (x2, y2).

Answer: –4

Slope formula

Substitution

Simplify.

Find the Slope of a Line

B. Find the slope of the line.

Substitute (0, 4) for (x1, y1) and

(0, –3) for (x2, y2).

Answer: The slope is undefined.

Slope formula

Substitution

Simplify.

Find the Slope of a Line

C. Find the slope of the line.

Answer:

Slope formula

Substitution

Simplify.

Substitute (–2, –5) for (x1, y1) and (6, 2) for (x2, y2).

Find the Slope of a Line

D. Find the slope of the line.

Answer: 0

Slope formula

Substitution

Simplify.

Substitute (–2, –1) for (x1, y1) and (6, –1) for (x2, y2).

A.

B.

C.

D.

A. Find the slope of the line.

A. 0

B. undefined

C. 7

D.

B. Find the slope of the line.

A.

B.

C. –2

D. 2

C. Find the slope of the line.

A. 0

B. undefined

C. 3

D.

D. Find the slope of the line.

Determine Line Relationships

Step 1 Find the slopes of and .

Determine whether and are parallel, perpendicular, or neither for F(1, –3), G(–2, –1), H(5, 0), and J(6, 3). Graph each line to verify your answer.

Determine Line Relationships

Step 2 Determine the relationship, if any, between the

lines.The slopes are not the same, so and are not parallel. The product of the slopes is

So, and are not

perpendicular.

Determine Line Relationships

Answer: The lines are neither parallel nor perpendicular.

Check When graphed, you can see that the lines are

not parallel and do not intersect in right angles.

A. parallel

B. perpendicular

C. neither

Determine whether AB and CD are parallel, perpendicular, or neither for A(–2, –1), B(4, 5), C(6, 1), and D(9, –2)

Use Slope to Graph a Line

First, find the slope of .

Slope formula

Substitution

Simplify.

Graph the line that contains Q(5, 1) and is parallel to MN with M(–2, 4) and N(2, 1).

Use Slope to Graph a Line

The slope of the line parallel to through Q(5, 1) is .

The slopes of two parallel lines are the same.

Graph the line.

Draw .

Start at (5, 1). Move up 3 units and then move left 4 units.

Label the point R.

Answer:

Graph the line that contains R(2, –1) and is parallelto OP with O(1, 6) and P(–3, 1).

A. B.

C. D. none of these