Section 3.4 Slope-Intercept Form of a Linear Equation 233 Given the equation of a line, we can write the equation in slope-intercept form by solving the equation for the y-variable.This is demonstrated in Example 2. Identifying the Slope and y-Intercept From a Linear Equation Example 2 Given the equation of the line 5x 2y 6, a. Write the equation in slope-intercept form. b. Identify the slope and y-intercept. Solution: a. Write the equation in slope-intercept form, y mx b, by solving for y. Add 5x to both sides. 5x 2y 6 2y 5x 6 2y 2 5x 6 2 2. Divide both sides by 5x 2 6 2 y 2 Divide each term by and simplify. Slope-intercept form y 5 2 x 3 10, 32. 52 b. The slope is , and the y-intercept is Skill Practice Given the equation of the line 2x 6y 3 . 4. Write the equation in slope-intercept form. 5. Identify the slope and the y-intercept. 2. Graphing a Line from Its Slope and y-Intercept Slope-intercept form is a useful tool to graph a line. The y-intercept is a known point on the line. The slope indicates the direction of the line and can be used to find a second point. Using slope-intercept form to graph a line is demonstrated in the next example. Graphing a Line Using the Slope and y-Intercept y 52 Example 3 Graph the equation of the line by using the slope and y-intercept. Solution: m 52 10, 32. x 3 First plot the y-intercept, The slope can be written as m 5 2 To find a second point on the line, start at the y-intercept and move down 5 units and to the right 2 units.Then draw the line through the two points (Figure 3-27). Answers 4. 5. slope is y-intercept is a0, 1 2 b 1 3 ; y 1 3 x 1 2 The change in y is 5. The change in x is 2. y 432 1 1 1 Figure 3-27 x 1 2 3 4 5 6 2 3 4 5 6 7 8 9 (0, 3) Start here 2 5
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