250 Chapter 3 Graphing Linear Equations in Two Variables Section 3.4 Slope-Intercept Form of a Linear Equation 1x1, y12 1x, y2 1x2, y22. Ax By C m 1y2 y12 1x2 x12 Sm m y b x mx ay b x b x mx y b mx b y b b y b x 0 Slope-Intercept Form of a Linear Equation is the slope-intercept form of a linear equation. y mx b m is the slope and the point (0, b) is the y-intercept. Identifying the Slope and y-Intercept from a Linear Equation For each equation, identify the slope and y-intercept. a. y 3x 1 b. y 2.7x 5 c. y 4x Solution: Each equation is written in slope-intercept form, The slope is the coefficient of x, and the y-intercept is determined by the constant term. a. The slope is 3. The y-intercept is (0,1). b. The slope is The y-intercept is (0, 5). c. can be written as The slope is 4. The y-intercept is (0, 0). y 3x 1 y 2.7x 5 2.7. y 4x y 4x 0. y mx b. Example 1 Concepts 1. Slope-Intercept Form of a Linear Equation 2. Graphing a Line from Its Slope and y-Intercept 3. Determining Whether Two Lines Are Parallel, Perpendicular, or Neither 4. Writing an Equation of a Line Using Slope-Intercept Form 1. Slope-Intercept Form of a Linear Equation In Section 3.2, we learned that the solutions to an equation of the form (where A and B are not both zero) represent a line in a rectangular coordinate system. An equation of a line written in this way is said to be in standard form. In this section, we will learn a new form, called slope-intercept form, that can be used to determine the slope and y-intercept of a line. Let (0, b) represent the y-intercept of a line. Let (x, y) represent any other point on the line (Figure 3-26). Then the slope of the line, m, can be found as follows: Let (0, b) represent , and let represent Apply the slope formula. Apply the slope formula. Simplify. Multiply by x to clear fractions. To isolate y, add b to both sides. mx b y or y mx b The equation is in slope-intercept form. Figure 3-26 x y (x, y) (0, b) Skill Practice Identify the slope and the y-intercept. 1. y 4x 6 2. y 3.5x 4.2 3. y 7 Classroom Examples: p. 256, Exercises 12 and 16 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 the next example. Answers 1. slope: 4; y-intercept: (0, 6) 2. slope: 3.5; y-intercept: (0, 4.2) 3. slope: 0; y-intercept: (0, 7)
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