Presentation on theme: "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."— Presentation transcript:
1 ObjectivesUse 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.
2 Identify the y-intercept. The y-intercept b is 1. Write the equation of the graphed line in slope-intercept form.Step 1Identify the y-intercept.The y-intercept b is 1.Step 2 Find the slope.Slope is = = – .riserun–343Step 3Write the equation in slope-intercept form.34y = – x + 1m = – and b = 1.34y = mx + bThe equation of the line is34y = – x + 1.
3 Write the equation of the graphed line in slope-intercept form.
4 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.
5 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.
6 Find the slope of the line. x481216y2511Let (x1, y1) be (4, 2) and (x2, y2) be (8, 5).The slope of the line is .34
7 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).
8 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.
9 In slope-intercept form, write the equation of the line that contains the points in the table. x–8–624y–5–11519First, find the slope.Next, choose a point, and use either form of the equation of a line.Method A Point-Slope FormMethod B Slope-intercept Form
11 Write the equation of the line in slope-intercept form with slope –5 through (1, 3). Method A Point-Slope Formy – 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 + 5Distribute.The equation of the slope is y = –5x + 8.y = –5x + 8Solve for y.
12 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 Formy = mx + bRewrite the equation using m and b.5 = (2)2 + b5 = 4 + by = 2x + 1y = mx + b1 = bThe equation of the line is y = 2x + 1.
13 Let x = selling price and y = rent. The table shows the rents and selling prices of properties from a game.Selling Price ($)Rent ($)75990121602625044Express 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).
14 Example 4A ContinuedTo 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.