Answer
A) y = x - 7
Step-by-step
Part 1: Convert to slope-intercept form
The equation -x + y = 5 has to be converted from standard form to slope-intercept form before we can begin solving this problem. The slope-intercept form is y = mx + b, where m is the slope of the line and b is its y-intercept. To convert it, just get y by itself on the left side.
-x + y = 5
y - x = 5
y - x + x = 5 + x
y = 5 + x
y = x + 5
This equation tells us the slope of the line (1) and the line's y-intercept (5)
Part 2: Find the equation of the line that is parallel to y = x + 5 and passes through the point (2, -5)
Parallel lines have equal slopes, so the slope of the line we are looking for will be 1 (or just x). So we can rule out answer choice D because it has a slope of -1 (or -x). To find the y-intercept for the line, we need to find the point where x = 0. We can work backwards with the rise over run method to find this point.
m = rise / run = change in y / change in x
1 = 1 / 1
We can use this information to perform a series of transformations (down 1 unit then left 1 unit) that will bring us to the y-intercept.
(2, -5) --> (1, -6)
(1, -6) --> (0, -7)
The point (0, -7) has an x-coordinate of 0, which means that the line intercepts the y-axis at this point.
The slope of the desired line is 1 and its y-intercept is -7.
Part 3: Substitute into the slope-intercept equation
y = mx + b
m = slope = 1 = x
b = y-intercept = -7
y = x - 7
