Question

Find the equation of the line through (-5,4) which is parallel to the line y=-x+6.

Give your answer in the form y=mx+b

Answer 1

`y = -x -1`

Explanation:

Given

Passed through (-5,4)

Parallel to: y=-x + 6

Required

Determine the line equation

If it is parallel to: y=-x + 6, then it means that they have the same slope.

A linear equation y = mx + b has the slope m.

So, by comparison of y = mx + b to y = -x + 6

`m = -1`

The line equation is then calculated as:

`y=m(x - x_1) + y_1`

Where

`m = -1`

`(x_1,y_1) = (-5,4)`

So:

`y = -1(x - (-5)) + 4`

`y = -1(x +5) + 4`

`y = -x -5 + 4`

`y = -x -1`