Holt Algebra 2 2-4 Writing Linear Functions Section 2.4 Writing Linear Functions

Holt Algebra 2

2-4 Writing Linear Functions

Section 2.4

Writing Linear Functions

Holt Algebra 2


Homework• Pg 121 #12-21, 47-49

Holt Algebra 2


Writing the Slope-Intercept Form of the Equation of a Line

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

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

Holt Algebra 2


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

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Step 3 Write the equation in slope-intercept form.

y = mx + b

34

y = – x + 1 m = – 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.

Step 1 Identify the y-intercept.The y-intercept b is 3.

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


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.

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). Choose any two points.


The slope of the line is .34

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Find the slope of the line shown.

Let (x1, y1) be (0,–2) and

(x2, y2) be (1, –2).

The slope of the line is 0.


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Find the slope of the line.x –6 –4 –2

y –3 –1 1

Let (x1, y1) be (–4, –1) and (x2, y2) be (–2, 1).

Choose any two points.


The slope of the line is 1.

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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.

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Writing Equations of Lines

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

x –8 –4 4 8

y –5 –3.5 –0.5 1

First, find the slope. Let (x1, y1) be (–8, –5) and (x2, y2) be (8, 1).

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

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

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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

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Holt Algebra 2


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)

Holt Algebra 2


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, .

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Holt Algebra 2 2-4 Writing Linear Functions Section 2.4 Writing Linear Functions