5.4 The Slope-Intercept Form

1. 5.4 The Slope-Intercept Form Objectives: Define and explain the components of the slope-intercept form of a linear equation. Use the slope-intercept form of a linear equation. Standards Addressed: 2.8.8.G: Represent relationships with tables or graphs. 2.8.8.H: Graph a linear function from a rule or table.

3. Ex. 1a.

4. b. Use the slope-intercept form to construct the graph of the equation y = 2x – 8. • M = 2/1 • B = (0, -8)

5. From 2 Points to an Equation • When you know 2 points on a line, you can determine the equation for that line. First, calculate the slope, m, by using the slope formula. Then calculate b by using the slope-intercept form and one of the points. • Recall from Lesson 5.2

6. Ex. 2a. A graph shows that after 3 hours of skating the total cost is $57. It also shows that after 5 hours of skating the total cost is $65. Write an equation in slope-intercept form for the line that models this situation. • M = -8/-2 = 4 • Y = 4x + b • 65 = 4(5) + b • 45 = b • Y = 4x + 45

7. Ex. 2b.

8. c. Write an equation in slope-intercept form for the line containing the points (3, 3) and (5, 7). • M = 2 • Y = 2x + b • 3 = 2(3) + b • 3 = 6 + b • B = -3 • Y = 2x – 3

9. Finding Intercepts • The slope-intercept form makes it very easy to find the y-intercept since it is given by b in the equation y = mx + b. You can also use this form to find the x-intercept, which is the x-coordinate of the point where the line crosses the x-axis.

10. Ex. 3

11. Ex. 4 Identify the x- and y-intercepts of each line. • A. • Y int = (0, -4) • X int = (4/3, 0) • B. • Y int = (0, 3) • X int = (3/5, 0)

12. Equations of Horizontal and Vertical Lines • The equation of a horizontal line is y = b, where b is the y-intercept. • The equation of a vertical line is x = a, where a is the x-intercept.

13. Ex. 5 Write an equation for each line. • A. * B. X = -3 Undefined Slope Y = 2 Zero Slope