250 Chapter 3 Linear Equations in Two Variables 1c. The slope is m = 0 and the value of b = 1. So, the equation is y = 0x + 1 or y = 1 1d. The graph crosses the y-axis at (0, -3), so b = -3. To determine the slope, we calculate the rise and run between the two points. The slope is m = rise run = 4 5 . So, the equation is y = 4 5 x - 3. 4 2 y –2 4 6 Rise 4 –4 –6 Student Check 1 Write the equation of the line that satisfies the given information. a. m = -2 and the y-intercept is (0, 9) b. m = 7 3 Run 5 2 (0, –3) (5, 1) and the y-intercept is (0, -1) c. m = 0 and the y-intercept is a0, 2 3 b d. x 6 4 2 y (0, 1) –4 –2 x 2 (2, 4) 4 –2 Use a Point and a Slope to Write an Equation of a Line When writing the equation of a line when the given point is not the y-intercept, we have to perform some work to determine the y-intercept and the value of b. There are two methods that we can use to determine the value of b. • One method uses the slope-intercept form of a line y = mx + b. • The other method uses another form of a line called the point-slope form. The point-slope form is derived from the slope formula using (x1, y1) as the given point and (x, y) as any other point on the line. m = y - y1 x - x1 Multiply both sides of the slope formula by the LCD = x - x1 to get the point-slope form of a line. y - y1 = m(x - x1) ������������������������ 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 the slope of the line. To write the equation of a line given a point and a slope, we will use one of the two methods described next. Objective 2 ▶ Write the equation of a line given a point and a slope.
hendricks_beginning_algebra_1e_ch1_3
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