Coordinate geometry problem: need help with exercise “d) the x-intercepts of the graphs in parts (a),(b) and (c).” I’m brushing up on algebra but I never studied math in English so I just don’t understand what is being asked here. I was able to solve the other problems. Thanks!

X-Intercept is the point at which the graph intersects the x-axis which is when y=0.

In 18 (a),(b), & (c), you have three separate lines, each with their own equations. In question (d), they are asking you to find (list) the x-intercepts of each of those three lines.

If it helps, I've answered these questions on GRE Prep Club: https://greprepclub.com/forum/in-the-xy-plane-nd-the-following-a-slope-and-y-intercep-13660.html#p33886

The x-intercept of a line is the point where your line crosses the x-axis .

In parts (a), (b) and (c), you are given three different lines. In part (d), you need to find the point where those lines cross the x-axis. Notice that any x-intercept, as a point, has 0 as the value of y-coordinate.

For (a), we already have the equation of the line, so all we have to do is substitute y = 0 into the equation:

2(0) + x = 6

x = 6

So, the x-intercept of the line 2y + x = 6 is (6, 0).

For (b), the equation of the described line is 3y - x = 3. Again you can find the x-intercept by substituting y = 0:

3(0) - x = 3

x = -3

So, the x-intercept of 3y - x = 3 is (-3, 0).

Finally, the equation of the line described in part (c) is y = 3x + 7. Again substituting y = 0, we find

0 = 3x + 7

x = -7/3.

So, the x-intercept of y = 3x + 7 is (-7/3, 0).