Definition/Procedure Example www.mhhe.com/messersmith Write the equation in slope-intercept form, and graph it. 6x 4y 16 4y 6x 16 y 6 4 x 16 4 y 3 2 x 4 Slope-intercept form m 3 2 , y-intercept (0, 4) Plot (0, 4), then use the slope to locate another point on the line. We will think of the slope as m 3 2 change in y change in x . x y 5 5 5 5 t 2 t t 2 1 The Slope-Intercept Form of a Line The slope-intercept form of a line is y mx b, where m is the slope and (0, b) is the y-intercept. If a line is written in slope-intercept form, we can use the y-intercept and the slope to graph the line. (p. 163) 4.3 Writing an Equation of a Line To write the equation of a line given its slope and y-intercept, use y mx b and substitute those values into the equation. (p. 172) Point-Slope Form of a Line: The point-slope form of a line is y y1 m(x x1), where (x1, y1) is a point on the line and m is its slope. Given the slope of the line and a point on the line, we can use the point-slope formula to fi nd an equation of the line. (p. 173) To write an equation of a line given two points on the line, a) use the points to fi nd the slope of the line then b) use the slope and either one of the points in the point-slope formula. (p. 174) Find an equation of the line with slope 3 and y-intercept (0, 8). y mx b y 3x 8 Substitute 3 for m and 8 for b. Find an equation of the line containing the point (1, 4) with slope 2. Express the answer in standard form. Use y y1 m(x x1). Substitute 2 for m. Substitute (1, 4) for (x1, y1). y (4) 2(x 1) y 4 2x 2 2x y 6 2x y 6 Standard form Find an equation of the line containing the points (2, 6) and (4, 2). Express the answer in slope-intercept form. m 2 6 4 (2) 4 6 2 3 We will use m 2 3 and the point (2, 6) in the pointslope formula. y y m(x x1) CHAPTER 4 Summary 217
messersmith_power_intermediate_algebra_1e_ch4_7_10
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