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Published byBrandon Tate Modified over 8 years ago

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

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**Identify the y-intercept. The y-intercept b is 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. Slope is = = – . rise run –3 4 3 Step 3 Write the equation in slope-intercept form. 3 4 y = – x + 1 m = – and b = 1. 3 4 y = mx + b The equation of the line is 3 4 y = – x + 1.

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

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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.

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**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.

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**Find the slope of the line.**

x 4 8 12 16 y 2 5 11 Let (x1, y1) be (4, 2) and (x2, y2) be (8, 5). The slope of the line is . 3 4

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**Find the slope of the line. x –6 –4 –2 y –3 –1 1**

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

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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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**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

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

Method A Point-Slope Form y – y1 = m(x – x1) y – (3) = –5(x – 1) Substitute. y – 3 = –5(x – 1) Simplify. Rewrite in slope-intercept form. y – 3 = –5(x – 1) y – 3 = –5x + 5 Distribute. The equation of the slope is y = –5x + 8. y = –5x + 8 Solve for y.

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**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). Method B Slope-Intercept Form y = mx + b Rewrite the equation using m and b. 5 = (2)2 + b 5 = 4 + b y = 2x + 1 y = mx + b 1 = b The equation of the line is y = 2x + 1.

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**Let x = selling price and y = rent.**

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).

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Example 4A Continued To find the equation for the rent function, use point-slope form. y – y1 = m(x – x1) Use the data in the first row of the table. Simplify.

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

parallel to y = 1.8x + 3 and through (5, 2) m = 1.8 y – 2 = 1.8(x – 5) y – 2 = 1.8x – 9 y = 1.8x – 7

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

Write the equation of the line in slope-intercept form. parallel to y = 5x – 3 and through (1, 4) perpendicular to y = ⅜x – 2 and through (3, 1)

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