BTGModeratorVI wrote: ↑Wed May 13, 2020 11:02 am
A line has a slope of 3/4 and intersects the point (-12, -39). At which point does this line intersect the x-axis?
A. (40,0)
B. (30,0)
C. (0,40)
D. (40,30)
E. (0,30)
Answer:
A
Solution:
If we let a be the x-intercept of the line, then (a, 0) is a point on the line. Since the slope of the line is 3/4 and another point on the line is (-12, -39), using the slope formula, we have:
(0 - (-39))/(a - (-12)) = 3/4
39/(a + 12) = 3/4
3(a + 12) = 4(39)
3a + 36 = 156
3a = 120
a = 40
Alternate Solution:
Using the slope-intercept form of the equation of a line, we know that the equation of the line is y = (3/4)x + b for some number b. To find b, we substitute (-12, -39) into the equation:
-39 = (3/4)(-12) + b
-39 = -9 + b
b = -30
So, the equation of the line is y = (3/4)x - 30. To find the x-intercept, we simply plug in y = 0:
0 = (3/4)x - 30
(3/4)x = 30
x = 40
Thus, the line crosses the x-axis at the point (40, 0).
Answer: A
