Question

The line passing through the points ( -4, 6) and ( b, 2) has a gradient 1 /2 . Find the value of b.

Answer 1

b = - 12

Explanation:

calculate the slope of the line passing through the 2 points and equate to
`(1)/(2)`

calculate the slope ( gradient ) m using the slope formula

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

with (x₁, y₁ ) = (4, 6 ) and (x₂, y₂ ) = (b, 2 )

m =
`(2-6)/(b-(-4))` =
`(-4)/(b+4)`

equating gives

`(-4)/(b+4)` =
`(1)/(2)` ( cross- multiply )

b + 4 = - 8 ( subtract 4 from both sides )

b = - 12