Question

Check each equation whose graph is the line that contains the points (4, –7) and (1, 5).

y = –4x + 9

y = –4x – 23

y – 1 = –4(x – 5)

y + 7 = –4(x – 4)

4x + y = 9

Answer 1

First find the slope: m = (5 - (−7)) / (1 - 4) = 12 / (−3) = −4. The line is y = −4x + 9 (or any equivalent form).

Check each:

- y = −4x + 9 — yes (matches).
- y = −4x − 23 — no (gives y = −27 at x=1, not 5).
- y − 1 = −4(x − 5) — no (expands to y = −4x + 21).
- y + 7 = −4(x − 4) — yes (expands to y = −4x + 9).
- 4x + y = 9 — yes (rearranges to y = −4x + 9).

So the correct equations are: y = −4x + 9; y + 7 = −4(x − 4); and 4x + y = 9.