Question

Which two points form a line that has a slope of 5/2?

A.) (3,6) and (-1,-4)
B.) (-4,2) and (7,-1)
C.) (-4,7) and (-9,5)
D.) (3,-7) and (8,4)​

Answer 1

To determine which two points form a line with a slope of 5/2, we can calculate the slope between each pair of points and see if any of them match 5/2.

Let's calculate the slopes for each option:

A.) (3,6) and (-1,-4):

slope = (y2 - y1) / (x2 - x1) = (-4 - 6) / (-1 - 3) = -10 / -4 = 5/2

B.) (-4,2) and (7,-1):

slope = (y2 - y1) / (x2 - x1) = (-1 - 2) / (7 - (-4)) = -3 / 11

C.) (-4,7) and (-9,5):

slope = (y2 - y1) / (x2 - x1) = (5 - 7) / (-9 - (-4)) = -2 / -5 = 2/5

D.) (3,-7) and (8,4):

slope = (y2 - y1) / (x2 - x1) = (4 - (-7)) / (8 - 3) = 11 / 5

From the calculations, we can see that only option A has a slope of 5/2. Therefore, the two points (3,6) and (-1,-4) form a line with a slope of 5/2.

Answer 2

A.) (3,6) and (-1,-4)

Explanation:

The slope of a line is calculated by dividing the change in y by the change in x. So, if two points have a slope of 5/2, then the change in y must be 5 and the change in x must be 2.

Let's look at each answer choice:

A. (3,6) and (-1,-4)

The change in y is 6 - (-4) = 10.

The change in x is 3 - (-1) = 4.

m = 10 / 4 = 5/2, so this answer choice is correct.

B. (-4,2) and (7,-1)

The change in y is 2 - (-1) = 3.

The change in x is 7 - (-4) = 11.

m = 3 / 11 , so this answer choice is not correct.

C. (-4,7) and (-9,5)

The change in y is 7 - 5 = 2.

The change in x is -9 - (-4) = -5.

m= 2 / -5 , so this answer choice is not correct.

D. (3,-7) and (8,4)

The change in y is 4 - (-7) = 11.

The change in x is 8 - 3 = 5.

m = 11 / 5 , so this answer choice is not correct.

Therefore, the two points that form a line that has a slope of 5/2 are (3,6) and (-1,-4)