Algebra 1 Section 6.3

Slope-Intercept Form The slope-intercept form of a linear equation is y = mx + b. m is the slope of the line. b is the y-coordinate of the y- intercept, (0, b).

Example 1 To write 3x + 2y = 6 in slope- intercept form, solve for y. 2y = 6 – 3x 3 2 y = 3 – x 3 2 y = - x + 3

Example 1 3 y = - x + 3 2 3 The slope is - . 2 The y-intercept is (0, 3).

Forms of Linear Equations Standard form: 3x + 2y = 6 Slope-intercept form: Function form: 3 2 y = - x + 3 3 2 f(x) = - x + 3

Slope-Intercept Form To change a linear equation to slope-intercept form: Solve the linear equation for y. Arrange terms on the right side with the variable term first.

Slope-Intercept Form The slope-intercept form of a line can be used to quickly graph the line. First, plot the y-intercept. Then, use the slope to plot one or more other points.

Example 2 Graph y = ½x + 4. The y-intercept is (0, 4). y x

Example 2 The slope is ½. Move up 1 and to the right 2. Another point could be added. Draw a line through the points. y x

Example 3 Write 2x + 3y = -3 as a linear function. 3y = -2x - 3 2 f(x) = - x – 1

Example 4 Write y = 3 in slope-intercept form. y = 0x + 3 The slope is 0. The y-intercept is 3.

Example 4 y = 0x + 3 y x

This is a constant function. Example 4 f(x) = 3 This is a constant function. x

Example 5 Let n = the number of pages. C(n) = 1.25n + 25 For a 23-page album: C(23) = 1.25(23) + 25 = $53.75

Homework: pp. 248-249