With geometry; will give how would i solve a problem such as the following: write an equation of the line that is parallel to -x + y = 5 and passes through the point (2, -5). a) y = x - 7 b) y = x - 5 c) y = x - 3 d) y = -x - 3

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