Question

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

Answer 1

Answer:

$y = -x -1$

Step-by-step 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:

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

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

$y = -x -5 + 4$

$y = -x -1$