b) Plot the point (0, 4). What does the slope, m 3, mean? m 3 3 1 change in y change in x To get from (0, 4) to another point on the line, we will move down 3 units in the y-direction and right 1 unit in the positive x-direction. We end up at (1, 1). Plot this point, and draw a line through (0, 4) and (1, 1). x y 5 1 1 t 1 t 5 5 5 In part b) we could have written m 3 as m 3 1 . This would have given us a different point on the same line. YOU TRY 4 Graph the line containing the point a) (1, 1) with a slope of 2 3 . b) (0, 5) with a slope of 3. c) (2, 2) with an undefi ned slope. We have already learned that a linear equation in two variables can be written in the form Ax By C (this is called standard form), where A, B, and C are real numbers and where both A and B do not equal zero. Equations of lines can take other forms, too, and now we will learn about one of those forms. In Example 5b, we graphed a line given its y-intercept, (0, 4), and its slope, 3. This leads us into another good method for graphing a line: We can express a line in slope-intercept form and then graph it using its slope and y-intercept. 6 Graph a Line Using Slope and y-Intercept We know that if (x1, y1) and (x2, y2) are points on a line, then the slope of the line is m y2 y1 x2 x1 Recall that to fi nd the y-intercept of a line, we let x 0 and solve for y. Let one of the points on a line be the y-intercept (0, b), where b is a number. Let another point on the line be (x, y). See the graph on the left. Substitute the points (0, b) and (x, y) into the slope formula. Subtract y-coordinates T m y2 y1 x2 x1 y b x 0 y b x c Subtract x-coordinates Solve m y b x for y. mx y b x x Multiply by x to eliminate the fraction. mx y b mx b y b b Add b to each side to solve for y. mx b y or y mx b Slope-intercept form x y b x y 162 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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