Question

A line that passes through the point (5,2) and is parallel to y=x

Answer 1

y = x - 3

Explanation:

Parallel lines have equal slopes.

The line y = x is written in the y = mx + b form, where m = 1, so the slope of the line y = x is 1. The slope of the parallel line is also 1.

The line you want has the form

y = mx + b

The slope is 1, so m = 1, and you get

y = 1x + b

y = x + b

We need to find the value of b.

Replace x and y in the equation with the x- and y-coordinates of the given point, respectively, and solve for b.

y = x + b

2 = 5 + b

b = -3

Now that we know b is -3, we replace b with -3

y = x - 3