Question

Is parallel to ? Explain.

no, because both lines have a slope of
no, because the slopes of the lines are not equal
yes, because both lines have a slope of
yes, because the slopes of the lines are not

Answer 1

I can’t tell from what you pasted because the two line equations (or coordinates) are missing. To decide if two lines are parallel you:

- Find each line’s slope (put in y = mx + b form or solve for y).
- If the slopes are equal and the lines have different y‑intercepts, the lines are parallel.
- If the slopes are equal and the y‑intercepts are also equal, the lines are the same (coincident).
- If the slopes are different, the lines are not parallel (they intersect).

Examples:
- Lines 2x + 3y = 6 and 4x + 6y = 12. Solve for y: y = −(2/3)x + 2 and y = −(2/3)x + 2. Slopes equal (−2/3) and intercepts equal, so they are the same line (not distinct parallel).
- Lines y = (1/2)x + 1 and 2y = x − 3 → y = (1/2)x − 3/2. Slopes equal (1/2) but intercepts different, so they are parallel.
- Lines y = x + 1 and y = 2x + 1 have slopes 1 and 2, so they are not parallel.

If you paste the two line equations from your problem, I’ll compute the slopes and tell you which of your multiple‑choice answers is correct.