Which of the following is an equation of line in the xy -plane above?

Options

A. x − y = −4
B. x−y= 4
C. x + y = −4
D. x + y = 4

Answer

C

Explanation

The equation defining any line can be written in the form , where m is the slope of the line and b is the y-coordinate of the y-intercept. Line ℓ passes through the point (0, −4), which is the y-intercept. Therefore, for line ℓ, b = −4. The slope of a line is the ratio of the difference between the y-coordinates of any two points to the difference between the x-coordinates of the same points. Calculating the slope using two points that line ℓ passes through, (−4, 0) and (0, −4), gives m = `(0-(-4))/((-4)-0)=4/(-4)` , or -1 Since m=-1 and b = −4, the equation of line ℓ can be written as y = (−1)x + (−4), or y = −x − 4. Adding x to both sides of y=-x-4 yields x+y=-4.
Choices A and B are incorrect. These equations both represent lines with a positive slope, but line ℓ has a negative slope. Choice D is incorrect. This equation represents a line that passes through the points (4, 0) and (0, 4), not the points (−4, 0) and (0, −4).