1 Write an Equation of a Line Given Its Slope and y-Intercept EXAMPLE 1 Find an equation of the line with slope 5 and y-intercept (0, 9). Remember, a y-intercept point will always have an x-value of 0. Procedure Write an Equation of a Line Given Its Slope and y-Intercept If we are given the slope and y-intercept of a line, use y mx b and substitute those values into the equation. Solution Since we are told the slope and y-intercept, use y mx b. m 5 and b 9 Substitute these values into y mx b to get y 5x 9. YOU TRY 1 Find an equation of the line with slope 2 3 and y-intercept (0, 6). 2 Use the Point-Slope Formula to Write an Equation of a Line Given Its Slope and a Point on the Line When we are given the slope of a line and a point on that line, we can use another method to fi nd its equation. This method comes from the formula for the slope of a line. Let (x1, y1) be a given point on a line, and let (x, y) be any other point on the same line. See Figure 4. The slope of that line is m y y1 x x1 Defi nition of slope m(x x1) y y1 Multiply each side by x x1. y y1 m(x x1) Rewrite the equation. We have found the point-slope form of the equation of a line. x y (x, y) Another point (x1, y1) Given point Figure 4 172 CHAPTER 4 Linear Equations in Two Variables and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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