Question

The points (-6, r)

and
(6,3) lie on a line with slope 3/4. Find the missing coordinate r.

Answer 1

r = -6

Explanation:

Equation of a line:

The equation of a line has the following format:

`y = mx + b`

In which m is the slope and b is the y-intercept.

Slope 3/4

This means that
`m = (3)/(4)`, and thus:

`y = (3)/(4)x + b`

(6,3)

This means that when
`x = 6, y = 3`. We use this to find b. So

`y = (3)/(4)x + b`

`3 = (3)/(4)(6) + b`

`b = 3 - (18)/(4) = (12)/(4) - (18)/(4) = -(6)/(4)`

So

`y = (3)/(4)x - (6)/(4) = (3x - 6)/(4)`

(-6, r)

r is y when
`x = -6`. So

`y = (3(-6) - 6)/(4) = -6`

So r = -6.