Entry Task

Write each function in slope-intercept form.

1. 4x + y = 8 2. –y = 3x 3. 2y = 10 – 6x

Determine whether each line is vertical or horizontal.

4. 5. y = 0

y = –4x + 8 y = –3x y = –3x + 5

3 4x =

vertical horizontal

I can use slope-intercept form and point-slope form to write linear functions.

2.4 More About Linear Equations

Example 1: Write the equation of the graphed line in slope-intercept form.

Step 1 Identify the y-intercept.The y-intercept b is 1.

Step 2 Find the slope.

Choose any two convenient points on the line, such as (0, 1) and (4, –2). Count from (0, 1) to (4, –2) to find the rise and the run. The rise is –3 units and the run is 4 units.

Slope is = = – . riserun

–34

34

3

–44

–3

Step 3 Write the equation in slope-intercept form.

34

y = – x + 1 m = – and b = 1. 34

Write the equation of the graphed line in slope-intercept form.

Your Turn

The equation of the line is 34

y = x + 3.

Example 2A: Finding the Slope of a Line Given Two or More Points

Find the slope of the line through (–1, 1) and (2, –5).

Let (x1, y1) be (–1, 1) and (x2, y2) be (2, –5).

Use the slope formula.

The slope of the line is –2.

Example 2B: Finding the Slope of a Line Given Two or More Points

Find the slope of the line.

x 4 8 12 16

y 2 5 8 11

Let (x1, y1) be (4, 2) and (x2, y2) be (8, 5). Choose any two points.

Use the slope formula.

The slope of the line is .34

Because the slope of line is constant, it is possible to use any point on a line and the slope of the line to write an equation of the line in point-slope form.

Method A Point-Slope Form

Rewrite in slope-intercept form.

Substitute.

Simplify.

Solve for y.

Distribute.

Write the equation of the line in slope-intercept form with slope –5 through (1, 3).

Check It Out! Example 3a

The equation of the slope is y = –5x + 8.

y – y1 = m(x – x1)

y – (3) = –5(x – 1)

y – 3 = –5(x – 1)

y – 3 = –5(x – 1)

y – 3 = –5x + 5

y = –5x + 8

Method B Slope-Intercept Form

Check It Out! Example 3bWrite the equation of the line in slope-intercept form through (–2, –3) and (2, 5).

First, find the slope. Let (x1, y1) be (–2,–3) and (x2, y2) be (2, 5).

y = mx + b

5 = (2)2 + b

5 = 4 + b

1 = b

Rewrite the equation using m and b.

y = mx + b y = 2x + 1

The equation of the line is y = 2x + 1.

Example 5A: Writing Equations of Parallel and Perpendicular Lines

Parallel lines have equal slopes.

Use y – y1 = m(x – x1) with (x1, y1) = (5, 2).

Distributive property.

Simplify.

m = 1.8

y – 2 = 1.8(x – 5)

y – 2 = 1.8x – 9

y = 1.8x – 7

Write the equation of the line in slope-intercept form.

parallel to y = 1.8x + 3 and through (5, 2)

Example 5B: Writing Equations of Parallel and Perpendicular Lines

Distributive property.

Simplify.

Use y – y1 = m(x – x1). y + 2 is equivalent to y – (–2).

Write the equation of the line in slope-intercept form.

perpendicular to and through (9, –2)

The slope of the given line is , so the slope of

the perpendicular line is the opposite reciprocal, .

Assignment # 14

Pg 86-88 #12-30 x 3, 49, 60-62

Example 4A: Entertainment ApplicationThe table shows the rents and selling prices of properties from a game. Selling Price

($)Rent ($)

75 9

90 12

160 26

250 44

Express the rent as a function of the selling price.

Let x = selling price and y = rent.

Find the slope by choosing two points. Let (x1, y1) be (75, 9) and (x2, y2) be (90, 12).

To find the equation for the rent function, use point-slope form.

Use the data in the first row of the table.

Simplify.

y – y1 = m(x – x1)

Example 4A Continued

Example 4B: Entertainment Application

Graph the relationship between the selling price and the rent. How much is the rent for a property with a selling price of $230?

To find the rent for a property, use the graph or substitute its selling price of $230 into the function.

Substitute.

The rent for the property is $40.

y = 46 – 6

y = 40

Write the equation of the line in slope-intercept form.

parallel to y = 5x – 3 and through (1, 4)

Parallel lines have equal slopes.

Use y – y1 = m(x – x1) with (x1, y1) = (5, 2).

Distributive property.

Simplify.

m = 5

y – 4 = 5(x – 1)

y – 4 = 5x – 5

y = 5x – 1

Check It Out! Example 5a

Distributive property.

Simplify.

Use y – y1 = m(x – x1). y + 2 is equivalent to y – (–2).

Check It Out! Example 5b

The slope of the given line is , so the slope of

the perpendicular, line is the opposite reciprocal .

Write the equation of the line in slope-intercept form.

perpendicular to and through (0, –2)

Lesson Quiz: Part I

y = –2x –1

y = 0.5x – 2

Write the equation of each line in slope-intercept form.

1.

2. parallel to y = 0.5x + 2 and through (6, 1)

3. perpendicular to and through (4, 4)

Lesson Quiz: Part II

Number in Group Cost ($)

4 98

7 134

15 230

4. Express the catering cost as a function of the number of people. Find the cost of catering a meal for 24 people.

f(x) = 12x + 50; $338