158 Chapter 2 Linear Equations in Two Variables and Functions Let (0, b) represent the y-intercept of a line. Let (x, y) represent any other point x 0 on the line where .Then the slope of the line through the two points is m m y2 y1 x2 x1 y b x m x ay b x mx y b S m b x y b x 0 y mx b The equation y 4x 7 is written in slope-intercept form. By inspection, we can see that the slope of the line is 4 and the y-intercept is (0, 7). Apply the slope formula. Simplify. Clear fractions. Simplify. mx b y or y mx b Solve for y: slope-intercept form Slope-Intercept Form of a Line is the slope-intercept form of a line. m is the slope and the point (0, b) is the y-intercept. y 5 mx 1 b Answer 1. Slope: 1 2 ; y-intercept: a0, 3 4 b y 1 2 x 3 4 Finding the Slope and y-Intercept of a Line Example 1 Given write the equation of the line in slope-intercept form.Then find the slope and y-intercept. Solution: Write the equation in slope-intercept form, y mx b, by solving for y. Subtract 3x from both sides. To isolate y, divide both sides by 4. 3 4 The slope is and the y-intercept is (0, 1). 3x 4y 4, 3x 4y 4 4y 3x 4 4y 4 3x 4 y 3 4 4 4 x 1 Skill Practice Write the equation in slope-intercept form. Determine the slope and the y-intercept. 1. 2x 4y 3 The slope-intercept form is a useful tool to graph a line. The y-intercept is a known point on the line, and 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 Example 2. x y m 1 (0, b)
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