Question 1

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

i) x-axis    
ii) y-axis

Select and check your answer...

A. y = -4 and x = 2
B. y = 2 and x = -4
C. y = 4 and x = -2
D. y = -2 and x = 4

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.

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 

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
 

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.