BTGmoderatorDC wrote: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)
TIP: If you were running short on time and encountered this question, you could quickly eliminate C, D and E and guess between A and B .
The coordinates of the x-intercept must be in the form (k,
0). So, we can eliminate C, D and E.
Now onto the solution...
Let's write the equation in slope y-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
We know the slope is 3/4, so we have: y = (3/4)x + b
Next, since the point (-12, -39) lies ON the line, the coordinates
x = -12 and
y = -39 must satisfy the equation of the line.
Plugging those values into our equation, we get:
-39 = (3/4)(
-12) + b = 0
Simplify: -39 = -9 + b
Solve for b to get: b = -30
So, the equation of the given line is: y = (3/4)x - 30
We want to find the coordinates of the x-intercept.
This is the point where y =
0.
So, plug y =
0 into the equation to get:
0 = (3/4)x - 30
[now solve for x]
Add 30 to both sides to get: 30 = (3/4)x
Multiply both sides by 4/3 to get: 40 = x
So, the coordinates of the x-intercept are (40,
0)
Answer: A
Cheers,
Brent
