In the xy-coordinate plane, line m is parallel to the x axis, and it passes through the point (4, -7). Which of the following is an equation for line m?
A. x = -4
B. y = 4
C. y = -7
D. y + 7 = x - 4
E. y – 7 = x + 4
Read the problem carefully. Take careful note that the line in the question is parallel to the x axis.
Identify the bottom line. equation for line m = ?
Assess your options. We must solve this problem by plugging the line into the point-slope formula. The point slope formula is:
Attack the problem. We need to use the point-slope formula, but to do so, we must determine the slope (m) and the y-intercept (b). It makes it a little easier to explain this problem if we draw out the line on the coordinate grid, but you do not have to do this step.
As the illustration shows, line m is parallel to the x axis, which makes it is a completely horizontal line. A horizontal line has a slope of 0. Think about it: if the y value never changes, then the change in y is zero, and no matter what the change in x, 0 divided by anything is 0. Since you know that the y value never changes, you also know the y-intercept will be (0,-7). Plug these values into the point-slope formula.
y = mx + b
y = (0)x -7
y = -7
Loop back. Verify that you solved for the bottom line.
The correct answer is C.
This is a medium level problem.