2 4 Writing Linear Functions Objectives Use slopeintercept

2 -4 Writing Linear Functions 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 slopeintercept 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 rise = – 3. run 4 4 Write the equation in slope-intercept form. 3 3 y = mx + b y=– x+1 m= – and b = 1. 4 4 3 The equation of the line is y = – x + 1. 4 Step 3 Holt Algebra 2

2 -4 Writing Linear Functions Write the equation of the graphed line in slope-intercept form. Holt Algebra 2

2 -4 Writing Linear Functions 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

2 -4 Writing Linear Functions Find the slope of the line through (– 1, 1) and (2, – 5). Let (x 1, y 1) be (– 1, 1) and (x 2, y 2) be (2, – 5). The slope of the line is – 2. Holt Algebra 2

2 -4 Writing Linear Functions Find the slope of the line. x y 4 2 8 5 12 8 Let (x 1, y 1) be (4, 2) and (x 2, y 2) be (8, 5). The slope of the line is 3. 4 Holt Algebra 2 16 11

2 -4 Writing Linear Functions 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). Holt Algebra 2

2 -4 Writing Linear Functions 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

2 -4 Writing Linear Functions In slope-intercept form, write the equation of the line that contains the points in the table. x – 8 – 6 2 y – 5 – 1 15 4 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

2 -4 Writing Linear Functions Holt Algebra 2

2 -4 Writing Linear Functions Write the equation of the line in slope-intercept form with slope – 5 through (1, 3). Method A Point-Slope Form y – y 1 = m(x – x 1) y – (3) = – 5(x – 1) y – 3 = – 5(x – 1) Substitute. Simplify. Rewrite in slope-intercept form. y – 3 = – 5(x – 1) y – 3 = – 5 x + 5 y = – 5 x + 8 Holt Algebra 2 Distribute. Solve for y. The equation of the slope is y = – 5 x + 8.

2 -4 Writing Linear Functions Write the equation of the line in slope-intercept form through (– 2, – 3) and (2, 5). First, find the slope. Let (x 1, y 1) be (– 2, – 3) and (x 2, y 2) be (2, 5). Method B Slope-Intercept Form y = mx + b Rewrite the equation 5 = (2)2 + b using m and b. 5=4+b y = mx + b y = 2 x + 1 1=b The equation of the line is y = 2 x + 1. Holt Algebra 2

2 -4 Writing Linear Functions The table shows the rents and selling prices of properties from a game. 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 (x 1, y 1) be (75, 9) and (x 2, y 2) be (90, 12). Holt Algebra 2 Selling Price Rent ($) 75 9 90 12 160 26 250 44

2 -4 Writing Linear Functions Example 4 A Continued To find the equation for the rent function, use point-slope form. y – y 1 = m(x – x 1) Use the data in the first row of the table. Simplify. Holt Algebra 2

2 -4 Writing Linear Functions Holt Algebra 2

2 -4 Writing Linear Functions Write the equation of the line in slope-intercept form. parallel to y = 1. 8 x + 3 and through (5, 2) m = 1. 8 y – 2 = 1. 8(x – 5) y – 2 = 1. 8 x – 9 y = 1. 8 x – 7 Holt Algebra 2

2 -4 Writing Linear Functions Write the equation of the line in slope-intercept form. Perpendicular to The slope of the given line is and through (9, – 2) , so the slope of the perpendicular line is the opposite reciprocal, Holt Algebra 2 .

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