Question

What is the value of k so that the line passing through (k, 6) and (1, 3) has a slope of m = 1?

a) k = 3
b) k = 4
c) k = 5
d) k = 6

Answer 1

The value of k for the line that has a slope of 1 and passes through (k, 6) and (1, 3) is 4.

Step-by-step explanation:

The student has asked to find the value of k such that the line passing through the points (k, 6) and (1, 3) has a slope (m) of 1. To find k, we can use the slope formula m = (y2 - y1) / (x2 - x1). In this case, x1=k, y1=6, x2=1, y2=3, and m=1. Plugging in these values gives us:

1 = (3 - 6) / (1 - k)

1 = -3 / (1 - k)

Therefore, (1 - k) = -3.

Solving for k gives us k = 4. Option b) k = 4 is the correct answer.