Question

Hi I need help knowing how to do question 17 :)

Answer 1

x + y - 3 = 0

Explanation:

The equation of a line when two points are given, it is given by the formula:

`$ (y - y_1)/(y_2 - y_1) = (x - x_1)/(x_2 - x_1) $`

where
`$ (x_1,y_1) $` and
`$ (x_2,y_2) $` are the two points passing through the line.

The two given points are:
`$ (x_1,y_1) = (-2,5) $`

`$ (x_2,y_2) = (5,-2) $`

Substituting the points in the formula, we get

`$ (y - 5)/(-2 -5) = (x + 2)/(5 + 2) $`

`$ \implies (y - 5)/(-7) = (x + 2)/(7) $`

`$ \implies y - 5 = -x - 2 $`

`$ \implies x + y - 3 = 0 $`

Therefore, the equation of the line passing through the two given points is x + y - 3 = 0.