MTH 030 -- Elementary Algebra -- Exercise Solutions
Section:
3.5

14-a)  Consider y = 0.5x - 3 and y = (1/2)x + 3. Because the two slopes are equal (0.5 = 1/2) and the y-intercepts are different (3 is not equal to -3), the graphs of these two equations are parallel lines.

14-b)  Consider y = 0.75x and y = (-4/3)x + 2. Because the two slopes are negative reciprocals of each other (0.75 = 3/4) ,the graphs of these two equations are perpendicular lines.

14-c)  Consider y = -x and y = x. Because the two slopes are negative reciprocals of each other ((1)(-1) = -1) ,the graphs of these two equations are perpendicular lines.

19)  The graph of y = 4x + 2 is a line with slope 4 and y-intercept (0, 2).

20)  The graph of y = -4x -2 is a line with slope -4 and y-intercept (0, -2)

21)  The graph of y = (x/4) -(1/2) is a line with slope 1/4 and y-intercept (0, -1/2 )

22)  The graph of y = 4x -2 is a line with slope 4 and y-intercept (0, -2)

23)  The graph of y = (1/2)x + 6 is a line with slope 1/2 and y-intercept (0, 6)

24)  The graph of y = 6 - xis a line with slope -1 and y-intercept (0, 6)

26)  The graph of y = 6x -1 is a line with slope 6 and y-intercept (0, -1)

27)  The graph of x + y = 8 is the graph of y = -x + 8 which is a line with slope -1 and y-intercept (0,8)

28)  The graph of x - y = -30 ( y = x + 30) is a line with slope 1 and y-intercept (0, 30)

30)  The graph of 3x - 5y = 15 (y = (3/5)x - 3) is a line with slope 3/5 and y-intercept (0, -3)

36) The equation of the line with slope 5 and y-intercept (0, -3) is y = 5x -3

38) The equation of the line with slope 1/3 and y-intercept (0, -5) is y = (1/3)x - 5

40) The equation of the line with slope -2 and y-intercept (0, 1) is y = -2x + 1

42) The equation of the line with slope (-7/6) and y-intercept (0, 2) is y = (-7/6)x + 2

46) The slope of the graph of the equation of y = x/3 is 1/3 and its y-intercept is (0, 0).

48) Find the slope and y-intercept of the graph of the equation 2x + 3y = 9.
Solution:    We want to write 2x + 3y = 9 in slope intercept form.
Begin by subtracting 2x from both sides to obtain 3y = -2x + 9
Then divide both sides of the equation by 3 to obtain
                
Clearly the slope is –2/3 and the y-intercept is (0, 3)

50) Find the slope and y-intercept of the graph of the equation 4x - 2y = 6.
Solution:    We want to write 4x - 2y = 6 in slope intercept form.
Begin by subtracting 4x from both sides to obtain 3y = -4x + 9
Then divide both sides of the equation by 3 to obtain y = 2x - 3.                 
Clearly the slope is 2 and the y-intercept is (0, -3)