Question

Given points (-3;-6), G(3; -2) and H(6; 1); determine:
(a) The equation of line FG

Answer 1

The equation of line FG is
`y = (2)/(3)x - 4`

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.

F(-3;-6), G(3; -2)

When we have two points, the slope is given by the change in y divided by the change in x. So

Change in y : -2 - (-6) = -2 + 6 = 4

Change in x: 3 - (-3) = 3 + 3 = 6

Slope:
`m = (4)/(6) = (2)/(3)`

So

`y = (2)/(3)x + b`

Finding b:

(3; -2) means that when
`x = 3, y = -2`. We use this to find b.

`y = (2)/(3)x + b`

`-2 = (2)/(3)(3) + b`

`2 + b = -2`

`b = -4`

The equation of line FG is
`y = (2)/(3)x - 4`