The line y = −x + 4 passes through which of the following points?

Correct — A. A point lies on a line when its coordinates satisfy the equation. Put each x into y = −x + 4 and compare with the printed y.

(2, 2): y = −2 + 4 = 2 ✓
(5, 4): y = −5 + 4 = −1 ✗
(1, 2): y = −1 + 4 = 3 ✗
(3, 6): y = −3 + 4 = 1 ✗

(2, 2) → option (a)

Why the others are wrong

• (b)
  (5, 4) — At x = 5 the line gives y = −5 + 4 = −1, not 4. The line has y = 4 at x = 0, its y-intercept (0, 4), and nowhere else.
• (c)
  (1, 2) — At x = 1 the line gives y = −1 + 4 = 3, not 2. The coordinates add to 3, and every point on this line has x + y = 4.
• (d)
  (3, 6) — At x = 3 the line gives y = −3 + 4 = 1, not 6. The coordinates add to 9, far from the x + y = 4 every point on the line obeys.

A line's equation is a test every point on it passes: a point (h, k) lies on y = mx + c exactly when k = mh + c.

Here m = −1 and c = 4. The line drops one unit for each unit it moves right, and crosses the y-axis at (0, 4).

Moving the x-term across gives the same line as x + y = 4. A point is on it when its coordinates add to 4, so each option takes one addition.

Key facts

• A point (h, k) lies on y = mx + c exactly when k = mh + c.
• y = −x + 4 rearranges to x + y = 4: slope −1, both intercepts 4.
• The line meets the axes at (0, 4) and (4, 0), and (2, 2) is their midpoint.

Common traps

• Treating the constant 4 as a y-value the line keeps. The line has y = 4 at a single point, the intercept (0, 4), which is why (5, 4) fails.
• Dropping the minus sign. With y = x + 4 no option passes, since (2, 2) would need y = 6, so if every option fails, re-read the sign first.

No directly related past PYQ was found.