Question

For what value of k does the straight line passing through the points

(4k+1,3k+2) and (3k+2,2k+1) have a slope of 2 ?

A) k=−1

B) k=0

C) k=1

D) k=2

Answer 1

The value of k that makes the slope of the line 2 is k = -3.

Step-by-step explanation:

To find the slope of a line passing through two points, we can use the formula:

Slope (m) = (y2 - y1) / (x2 - x1)

Using the points (4k+1,3k+2) and (3k+2,2k+1), we can substitute these values into the formula to determine the slope:

m = [(2k+1) - (3k+2)] / [(3k+2) - (4k+1)] = (2k+1 - 3k - 2) / (3k+2 - 4k-1) = (-k - 1) / (-k + 1)

We are given that the slope is 2, so we can set this equal to 2 and solve for k:

2 = (-k - 1) / (-k + 1)

-2k + 2 = -k - 1

k = -3

Therefore, the value of k that makes the slope of the line 2 is k = -3, option A.