Math Expression: Equation of line parallel to the x-axis or y-axis practice

Determine the equation of a line that pass through the point (4,-2) that is parallel to the:

Step 1

As for the start, it is better to plot the point (4,-2) on the coordinate plane to have a clearer picture of this question.
Step 2

Now, for the line that is parallel to the x-axis and passes through the line (4,-2), we can just draw a horizontal line as shown in the picture.

Also, notice that all the points on the line have the y-coordinates of -2. Hence, this line can be represented with the equation:

y = -2
Step 3

Similarly, for the line that passes through (4,-2) and parallel to the y-axis, we can draw a vertical line as shown in the picture.

Again, all the points on the line have the x-coordinate of 4. Hence, we can write the equation for this line as:

x = 4
Step 4

From Step 1 and Step 2, we have the equation of the line as:

y = -2 (parallel to the x-axis)
x = 4 (parallel to the y-axis)

Clearly the answer is D.