Question

The line AB passes through the points A(-3, 4) and (k, 12).

The gradient of AB is 4.
Work out the value of k.

Answer 1

k = - 1

Explanation:

calculate the gradient (slope) m of AB using the slope formula and equate to 4

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 3, 4 ) and (x₂, y₂ ) = (k, 12 )

m =
`(12-4)/(k-(-3))` =
`(8)/(k+3)` , then

`(8)/(k+3)` = 4 ( multiply both sides by (k + 3 ) )

4(k + 3) = 8 ( divide both sides by 4 )

k + 3 = 2 ( subtract 3 from both sides )

k = - 1