Five-Minute Check (over Lesson 2–3)

CCSS

Then/Now

New Vocabulary

Key Concept:Slope-Intercept Form

Example 1:Write an Equation in Slope-Intercept Form

Key Concept:Point-Slope Form

Example 2:Write an Equation Given Slope and One Point

Example 3:Standardized Test Example

Key Concept:Parallel and Perpendicular Lines

Example 4:Write an Equation of a Perpendicular Line

Over Lesson 2–3

Find the rate of change for the data.

Find the slope of the line that passes through points (2.3, 9.5) and (3.8, 20).Find the slope of the line that passes through points (3, 5) and (–6, 5).Determine the rate of change of the graph.

Graph

Over Lesson 2–3

Find the rate of change for the data.

A. –22 mi/gal

B.mi/gal

C. mi/gal

D. 22 mi/gal

Over Lesson 2–3

Find the slope of the line that passes through points (2.3, 9.5) and (3.8, 20).

A. –7

B.

C. 7

D.

Over Lesson 2–3

A. –1

B. 0

C. 1

D. 3

Find the slope of the line that passes through points (3, 5) and (–6, 5).

Over Lesson 2–3

Determine the rate of change of the graph.

A. –3

B.

C.

D. 3

Content Standards

A.SSE.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Mathematical Practices

2 Reason abstractly and quantitatively.

You determined slopes of lines.

• Write an equation of a line given the slope and a point on the line.

• Write an equation of a line parallel or perpendicular to a given line.

• slope-intercept form

• point-slope form

• parallel

• perpendicular

Write an Equation in Slope-Intercept Form

Write an equation in slope-intercept form for the line.

Step 1 Find the slope.

Slope formula

(x1, y1) = (–1, 4), (x2, y2) = (2, 3)

Simplify.

••

Write an Equation in Slope-Intercept Form

Step 2 Use the slope and a point to find the y-intercept.

Slope-intercept form

Simplify.

The y-intercept is

Write an Equation in Slope-Intercept Form

Step 3 Substitute the values into the slope-interceptequation.

Slope-intercept form

A.

B.

C.

D.

Write an equation in slope-intercept form for the line.

Write an Equation Given Slope and One Point

Point-slope form

Simplify.

Write an Equation Given Slope and One Point

Answer:

Subtract 2 from each side.

A.

B.

C.

D.

What is an equation of the line through (2, –3) and (–3, 7)?

Read the Test ItemYou are given the coordinates of two points on the line.

A

B

C

D

Solve the Test Item

Step 1 Find the slope of the line.

The slope is –2. That eliminates choices B and C.

Slope formula

(x1, y1) = (2, –3), (x2,y2) = (–3, 7)

Simplify.

Step 2 Write an equation. Use either ordered pairfor (x1, y1).

Answer: D

Point-slope form

m = –2; (x1, y1) = (2, –3)

Simplify.

Subtract 3 from each side.

Which is an equation of the line that passes through (2, 5) and (–1, 3)?

A.

B.

C.

D.

Write an Equation of a Perpendicular Line

Write an equation in slope-intercept form for the line that passes through (3, –2) and is perpendicular to the line whose equation is y = –5x + 1.

Write an Equation of a Perpendicular Line

Answer:

Distributive Property

Point-slope form

Subtract 2 from each side.

A.

B.

C.

D.