Section 3.3 The Slope of a Line 235 4b. Find the slope of 5x + y = 10. �������������������������������������� ���������������������������������������������������������������� The equation is not in slope-intercept form, so we cannot conclude the slope is 5. We must first solve the equation for y. 5x + y = 10 5x + y - 5x = 10 - 5x y=-5x + 10 coeffic s 5, so the slope . The coefficient of x is -5. So, the slope m = -5. 4c. Graph the line y = 1 2 x - 1. �������������������������������������� ���������������������������������������������������������������� The slope was used incorrectly to obtain the graph. Since the slope of y = 1 2 x - 1 is 1 2 , we move up 1 unit as we move right 2 units. The coefficient of x is slope m = 5. Begin at (0, -1) and then move right 1 and up 2 since slope is 1 2 . 1 1 2 (1, 1) 1 2 3 –1 –1 –2 x (0, –1) (2, 0) 1 2 2 3 –1 –1 –2 x y (0, –1) e the s y 0 1 ANSWERS TO STUDENT CHECKS Student Check 1 a. m = 0 b. m=- 3 5 c. m = 4 d. undefined e. m = 2 3 Student Check 2 a. m = 7 ( y increases by 7 units as x increases by 1 unit); (0, 8) b. m = 1 5 ( y increases by 1 unit as x increases by 5 units); (0, 0) c. y = 9x - 5; m = 9 ( y increases by 9 units as x increases by 1 unit); (0, -5) d. y=- 1 2 x + 5; m=- 1 2 ( y decreases by 1 unit as x increases by 2 units); (0, 5) e. can’t be written in slope-intercept form, slope is undefined f. y = 0x - 2; m = 0 ( y doesn’t change as x increases by 1 unit); (0, -2) Student Check 3 a. b. (0, 3) (4, 4) 6 2 –2 2 x 4 4 6 –2 y 8 2 2 4 (1, 3) (0, 6) y –4 –2 4 x ���������������������������������������������� 1. The slope of a line is a measure of the steepness of the line. It is defined as the ratio of the change in y to the change in x. 2. The slope of a line can be found using its equation, using a table of solutions, using its graph, or using the slope formula. • To find the slope given its equation, the equation must be in slope-intercept form y = mx + b. The coefficient of x is the slope. • From a table of solutions, we can find the change in the y-values and the change in the x-values between the points. The ratio of these changes is the slope. • From a graph, we can find the slope by determining the vertical change and the horizontal change between two points on the graph. The ratio of the vertical change to the horizontal change is the slope.
hendricks_beginning_algebra_1e_ch1_3
To see the actual publication please follow the link above