Question

A line has a gradient -6 and passes through the points with coordinates (1,6) and (b,7). Find the value of b.

Answer 1

b =
`(5)/(6)`

Explanation:

Calculate the slope m using the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (1, 6) and (x₂, y₂ ) = (b, 7)

m =
`(7-6)/(b-1)`

=
`(1)/(b-1)` = - 6 ( multiply both sides by (b - 1) )

- 6(b - 1) = 1

- 6b + 6 = 1 ( subtract 6 from both sides )

- 6b = - 5 ( divide both sides by - 6 )

b =
`(5)/(6)`