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hendricks_beginning_algebra_1e_ch1_3

232 Chapter 3 Linear Equations in Two Variables 2e. The equation y = 3 is the equation of a horizontal line. It is in slope-intercept form and is equivalent to y = 0x + 3. The coefficient of x is 0, so the slope is m = 0. The constant term is 3, so the y-intercept is (0, 3). The slope m = 0 = 0 1 . This means that there is no change in the y-values as the x-values increase by 1 unit. 2f. The equation x = 2 represents a vertical line through the point (2, 0). It cannot be written in slope-intercept form since there is no y-variable. From Example 1, we know that the slope of a vertical line is undefined. There is no y-intercept since the graph doesn’t cross the y-axis. Note that we can use the slope formula to find the slope using two points on the line, such as (2, 0) and (2, 3). m = y2 - y1 x2 - x1 State the slope formula. m = 3 - 0 2 - 2 Let (x1, y1) = (2, 0) and (x2, y2) = (2, 3). m = 3 0 Simplify. m is undefined. Student Check 2 Write the equation in slope-intercept form, if possible. State the slope and y-intercept of the line from its equation. Explain how the x- and y-values change with respect to one another. a. y = 7x + 8 b. y = 1 5 x c. 9x - y = 5 d. x + 2y = 10 e. x = -4 f. y = -2 �������������������� Slopes of Vertical and Horizontal Lines The slope of the equation x = h, where h is a real number, is undefined. The slope of the equation y = k, where k is a real number, is zero. ���������� To remember the slopes of horizontal and vertical lines, we can think of the following situation: If we can walk on the line, then the line has a slope. If we can’t walk on the line, then the slope is undefined. Since we cannot “walk” on a vertical line, it has a slope that is undefined. We walk on horizontal “lines” every day, so the slope of a horizontal line is a real number, the real number 0. Graph a Line Using Its Slope and y-Intercept In Section 3.2, we graphed a line by finding at least two points on the line. We can also graph a line if we know its slope and y-intercept. • The y-intercept (0, b) is one point on the line. • Another point can be obtained from the slope. Objective 3 ▶ Graph a line given its slope and y-intercept.


hendricks_beginning_algebra_1e_ch1_3
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