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

Question

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 · Answer

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 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 _________________ Manhattan Review GMAT Prep Locations: Manhattan Review Mumbai | Hyderabad | GRE Prep Warangal | Begumpet GRE Coaching | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

Scott@TargetTestPrep · Answer

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

deloitte247 · Answer

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

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

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

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

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

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