What is an equation of the line that passes through the point (−1,5) and is parallel to the line
x−y=6?

The equation in slope-intercept form is y = x + 6

Step-by-step explanation:

For this question, we will use point slope form, where you can put in a point and a slope and get an equation of the line that passes through the point with that slope.

The point slope formula is y - y1 = m(x-x1) where y1 is the y coordinate of the point, m is the slope, and x1 is the x coordinate.

We are trying to find a line parallel to x - y = 6, so our line will have the same slope as it. To find the slope of x - y = 6, subtract x and divide by -1. This gives us y = x - 6, where the slope is 1.

Now we have all necessary information.

Plug in the values: y - 5 = 1(x + 1)

Simplify: y - 5 = x + 1

Add 5 to both sides: y = x + 6

The answer is y = x + 6