Five-Minute Check (over Lesson 4–2)

CCSS

Then/Now

New Vocabulary

Key Concept: Point-Slope Form

Example 1: Write and Graph an Equation in Point-Slope Form

Concept Summary: Writing Equations

Example 2: Writing an Equation in Standard Form

Example 3: Writing an Equation in Slope-Intercept Form

Example 4: Point-Slope Form and Standard Form

Over Lesson 4–2

A. y = 22x + 3

B. y = 22x – 3

C. y = 3x + 22

D. y = 3x – 22

Write an equation of the line that passes through the given point and has the given slope. (5, –7), m = 3

Over Lesson 4–2

5-Minute Check 2

Write an equation of the line that passes through the given point and has the given slope.

(1, 5),

A.

B.

C.

D.

Over Lesson 4–2

A. y = –3x + 1

B. y = –3x

C. y = –3

D. y = 3x

Which equation is the line that passes through the points (6, –3) and (12, –3)?

Over Lesson 4–2

Which equation is the line that passes through the points (9, –4) and (3, –6)?

A. y = –3x – 7

B.

C.

D. y = x + 7

Over Lesson 4–2

A. y = –2x + 4

B. y = 2x + 4

C. y = 2x – 4

D. y = 4x – 2

Identify the equation for the line that has an x-intercept of –2 and a y-intercept of 4.

Over Lesson 4–2

Which is an equation of the graph shown?

A.

B.

C. y = –2x + 3

D. y = 2x + 3

Content Standards

F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Mathematical Practices

2 Reason abstractly and quantitatively.

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

You wrote linear equations given either one

point and the slope or two points.

• Write equations of lines in point-slope form.

• Write linear equations in different forms.

Write and Graph an Equation in Point-Slope Form

(x1, y1) = (–2, 0)

Point-slope form

Answer:

Write the point-slope form of an equation for a line

that passes through (–2, 0) with slope

Simplify.

Write and Graph an Equation in Point-Slope Form

Answer:

Graph the equation

Plot the point at (–2, 0).

Use the slope to find another point on the line. Draw a line through the two points.

A. y – 4 = –2(x + 3)

B. y + 3 = –2(x – 4)

C. y – 3 = –2(x – 4)

D. y + 4 = –2(x – 3)

Write the point-slope form of an equation for a line that passes through (4, –3) with a slope of –2.

In standard form, the variables are on the left side of the equation. A, B, and C are all integers.

Multiply each side by 4 to eliminate the fraction.

Original equation

Distributive Property

Writing an Equation in Standard Form

Writing an Equation in Standard Form

4y – 3x = 3x – 20 – 3x

–3x + 4y = –20

Answer: The standard form of the equation is 3x – 4y = 20.

Simplify.

Subtract 3x from each side.

3x – 4y = 20 Multiply each side by –1.

A. –2x + y = 5

B. –2x + y = 11

C. 2x – y = –11

D. 2x + y = 11

Write y – 3 = 2(x + 4) in standard form.

Writing an Equation in Slope-Intercept Form

Distributive Property

Original equation

Add 5 to each side.

Writing an Equation in Slope-Intercept Form

Simplify.

Answer: The slope-intercept form of the equation is

Write 3x + 2y = 6 in slope-intercept form.

A.

B. y = –3x + 6

C. y = –3x + 3

D. y = 2x + 3

Point-Slope Form and Standard Form

A. GEOMETRY The figure shows trapezoid ABCDwith bases AB and CD.

Write an equation in point-slope form for the line containing the side BC.

___

Point-Slope Form and Standard Form

Step 1 Find the slope of BC.

Slope formula

(x1, y1) = (4, 3) and

(x2, y2) = (6, –2)

Point-Slope Form and Standard Form

Step 2 You can use either point for (x1, y1) in the point-slope form.

Using (4, 3) Using (6, –2)

y – y1 = m(x – x1) y – y1 = m(x – x1)

Point-Slope Form and Standard Form

B. Write an equation in standard form for the same line.

Answer: 5x + 2y = 26

Original equation

Distributive Property

Add 3 to each side.

Multiply each side by 2.

Add 5x to each side.

2y = –5x + 26

5x + 2y = 26

A. y – 6 = 1(x – 4)

B. y – 1 = 1(x + 3)

C. y + 4 = 1(x + 6)

D. y – 4 = 1(x – 6)

A. The figure shows right triangle ABC. Write the point-slope form of the line containing the hypotenuse AB.

A. –x + y = 10

B. –x + y = 3

C. –x + y = –2

D. x – y = 2

B. The figure shows right triangle ABC. Write the equation in standard form of the line containing the hypotenuse.

Homework:

Pg 236 #11-33 odd