Section 3.3 The Slope of a Line 231 �� ������������������������ ������������������ 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. 2a. y = 4x + 1 2b. y=- 2 3 x 2c. 6x - y = 2 2d. 4x + 3y = 24 2e. y = 3 2f. x = 2 Solutions 2a. The equation y = 4x + 1 is in slope-intercept form since it is solved for y. The coefficient of x is 4, so the slope is m = 4. The constant term is 1, so the y-intercept is (0, 1). The slope, m = 4 = 4 1 , means that as the y-values increase by 4 units, the x-values increase by 1 unit. 2b. The equation, y = - 2 3 x + 0, is in slope-intercept form since it is solved for y. The coefficient of x is - 2 3 , so, the slope is m=- 2 3 . The constant term is 0, so the y-intercept is (0, 0). The slope m=- 2 3 = -2 3 or 2 -3 . This means that as the y-values decrease by 2 units, the x-values increase by 3 units. An equivalent way to state this is that as the y-values increase by 2 units, the x-values decrease by 3 units. 2c. We must solve the equation for y to write it in the slope-intercept form. 6x - y = 2 6x - y - 6x = 2 - 6x Subtract 6x from each side. -y=-6x +2 Simplify. -1(-y) = -1(-6x + 2) Multiply each side by -1. y = 6x - 2 Simplify. The coefficient of x is 6, so the slope is m = 6. The constant term is -2, so the y-intercept is (0, -2). The slope m = 6 = 6 1 . This means that as the y-values increase by 6 units, the x-values increase by 1 unit. 2d. We must solve the equation for y. 4x + 3y = 24 4x + 3y - 4x = 24 - 4x Subtract 4x from each side. 3y=-4x + 24 Simplify. 3y 3 = -4x + 24 3 Divide each side by 3. y = - 4 3 x + 8 Simplify. The coefficient of x is - 4 3 , so the slope is m=- 4 3 . The constant term is 8, so the y-intercept is (0, 8). The slope m=- 4 3 = -4 3 or 4 -3 . This means that as the y-values decrease by 4 units, the x-values increase by 3 units. An equivalent way to state this is that as the y-values increase by 4 units, the x-values decrease by 3 units.
hendricks_beginning_algebra_1e_ch1_3
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