Question

The line passing through (-3 , -6) and (d, -5d) has a gradient of -3.

Find the value of d.

Answer 1

Answer is the picture

Answer 2

d = 7.5

Explanation:

Calculate the slope m using the slope formula and equate to - 3

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

with (x₁, y₁ ) = (- 3, - 6) and (x₂, y₂ ) = (d, - 5d)

m =
`(-5d+6)/(d+3)` = - 3 ( multiply both sides by (d + 3) )

- 5d + 6 = - 3(d + 3)

- 5d + 6 = - 3d - 9 ( add 3d to both sides )

- 2d + 6 = - 9 ( subtract 6 from both sides )

- 2d = - 15 ( divide both sides by - 2 )

d = 7.5