Question

If anyone could help me with this I'd be really grateful.

A is the point of coordinates (4,6)

B is the point with coordinates (d,21)

The gradient of the line AB is 3

Work out the value of D

Please provide a explanation

Answer 1

d = 9

Explanation:

Calculate the slope m of line AB and equate the result to 3

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

with (x₁, y₁ ) = A(4, 6) and (x₂, y₂ ) = B(d, 21)

m =
`(21-6)/(d-4)` =
`(15)/(d-4)` = 3 ( multiply both sides by d - 4 )

15 = 3(d - 4), that is

15 = 3d - 12 ( add 12 to both sides )

27 = 3d ( divide both sides by 3 )

9 = d