230 Chapter 3 Linear Equations in Two Variables Student Check 1 Use the slope formula to determine the slope of the line between each pair of points. a. (1, -6) and (7, -6) b. (-2, 5) and (3, 2) c. (4, 7) and (2, -1) d. (-4, 2) and (-4, -1) e. 4 2 2 –2 –8 –6 –4 –2 –4 x y The Slope-Intercept Form of a Line In the previous objective, we found that the slope of the line y = 2x - 4 is m = 2 1 = 2. We discovered this by examining the ratio of the vertical change to the horizontal change using the table on page 226. We can also confirm this by substituting two points that lie on the line into the slope formula. For instance, (0, -4) and (3, 2) lie on the line. m = y2 - y1 x2 - x1 State the slope formula. m = 2 - (-4) 3 - 0 Let (x1, y1) = (0, -4) and (x2, y2) = (3, 2). m = 6 3 Simplify. m =2 Simplify. The ordered pair (0, -4) is the y-intercept of the graph of y = 2x - 4 since its x-coordinate is zero. Note that the value of the slope and the y-intercept are provided in the equation, y = 2x - 4. The coefficient of x, 2, is the same as the slope of the line. The constant term, -4, is the same as the y-coordinate of the y-intercept of the line. The equation y = 2x - 4 is in what we call the slope-intercept form of a line. �������������������� The Slope-Intercept Form of a Line The equation y = mx + b is the slope-intercept form of a linear equation. The value m is the slope of the line and the point (0, b) is the y-intercept. y = m x + b Slope y-intercept The key difference between the standard form of a linear equation and the slopeintercept form of a linear equation is that the slope-intercept form is the equation solved for y. ���������������������� Finding the Slope and y-Intercept of a Linear Equation Step 1: Solve the linear equation for y, if necessary. Step 2: The coefficient of x is the slope of the line. Step 3: The constant term is the y-coordinate of the y-intercept of the line. Objective 2 ▶ Use the slope-intercept form of a line to find its slope and y-intercept.
hendricks_beginning_algebra_1e_ch1_3
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