Holt Algebra 2 2-4 Writing Linear Functions Use slope-intercept form and point-slope form to write...

Holt Algebra 2

2-4 Writing Linear Functions

Use slope-intercept form and point-slope form to write linear functions.Write linear functions to solve problems.

Objectives

Recall from Lesson 2-3 that the slope-intercept form of a linear equation is y= mx + b, where m is the slope of

the line and b is its y-intercept.

Holt Algebra 2

2-4 Writing Linear Functions 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.

Slope is = = – . riserun

–34

34

Step 3 Write the equation in slope-intercept form.

y = mx + b 34

y = – x + 1m = – and b = 1. 34

The equation of the line is 34

y = – x + 1.

Holt Algebra 2


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

Holt Algebra 2


Notice that for two points on a line, the rise is the differences in the y-coordinates, and the run is the differences in the x-coordinates. Using this information, we can define the slope of a line by using a formula.

Holt Algebra 2


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

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

The slope of the line is –2.

Holt Algebra 2


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).

The slope of the line is .34

Holt Algebra 2


Find the slope of the line. x –6 –4 –2

y –3 –1 1

Find the slope of the line through (2,–5) and (–3, –5).

Find the slope of the line shown.

Holt Algebra 2


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.

Holt Algebra 2


In slope-intercept form, write the equation of the line that contains the points in the table.

x –8 –6 2 4

y –5 –1 15 19

First, find the slope.

Next, choose a point, and use either form of the equation of a line.

Method A Point-Slope Form

Method B Slope-intercept Form

Holt Algebra 2


Holt Algebra 2


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).

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

Holt Algebra 2


Method B Slope-Intercept Form

Write 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.

Holt Algebra 2


The 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).

Holt Algebra 2


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

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Holt Algebra 2


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)

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Perpendicular to and through (9, –2)

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

the perpendicular line is the opposite reciprocal, .

Holt Algebra 2



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

perpendicular to y = ⅜x – 2 and through (3, 1)

Holt Algebra 2 2-4 Writing Linear Functions Use slope-intercept form and point-slope form to write...

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