A line has a slope of 3/4 and intersects the point (-12, -39). At which point does this line intersect the x-axis?

[BTGModeratorVI]

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
Source: Manhattan Prep

[Jay@ManhattanReview]

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
Source: Manhattan Prep

If a line passes through two points (x1, y1) and (x2, y2), then the slope m of the line is given by

m = (y2 – y1)/(x2 – x1)

We already know that m = 3/4 and x1 = –12 and y1 = –39

Let's go each option one by one and see which one works.

A. (40,0): (y2 – y1)/(x2 – x1) = (0 + 39)/(40 + 12) = 39/52 = 3/4 = m. Correct.

There's no need to check other options.

B. (30,0)
C. (0,40)
D. (40,30)
E. (0,30)

The correct answer: A

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

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

[deloitte247]

Slope = 3/4
Points are given as ( -12, -39)
Therefore, point on y-axis = -39
Point on x-axis = -0

Question => At which point does this line intersect the x-axis?

Equation of line is given as y = mx + c
Where y = point on y-axis
x = point on x axis
m = slope and;
c = intercept

Slothing our values =>
-39 = (3/4 * -12) + c
-39 = -9 + c
c = -39 + 9 = -30
Equation of line becomes y = 3/4 (x) + (-30)

The intersection of line at x-axis is called x-intercept
Let y = 0
0 = 3/4(x) + (-30)
0 = 3/4(x) - 30
$$\frac{\frac{3}{4}\left(x\right)}{\frac{3}{4}}=\frac{30}{\frac{3}{4}}$$
$$x=30\cdot\frac{4}{3}$$
$$x=10\cdot4=40$$
y = 0 and x = 40
The x and y coordinate = (40, 0)

Answer = A