If a line has a slope of 1/2 and passes through the points (3,k) and (7,1) what is the value of k

Answer 1

Hi...

Recall that slope, m = rise / run OR (change in y) / (change in x)

The change in y is (y₂ - y₁) and the change in x is (x₂ - x₁) with (x₁, y₁) being the coordinates of the 1st point P₁ and (x_2, y₂) being the coordinates of the 2nd point P₂

Say P₁ = (3, k) and P₂ = (7, 1) ....does NOT matter which is which as the slope will be the SAME

¹/₂ = (y₂ - y₁) / (x₂ - x₁)

¹/₂ = (1 - k) / (7 - 3)

¹/₂ = (1 - k) / 4

Cross multiply and solve for x

2(1 - k) = (1)(4)

2 - 2k = 4

-2k = 4 - 2

-2k = 2

k = -1

Check by recalculating the slope with (3, -1) and (7, 1)

Hope this helps...