The graph of y = 4x − 5 passes through which point?

Correct — D.
Substitute each x into y = 4x − 5 and compare with the point's y.

(1, −1): 4(1) − 5 = −1, matches
(0, −5): 4(0) − 5 = −5, matches
(2, 3): 4(2) − 5 = 3, matches

All three points lie on the line → option (d), All the above.

Why the others are wrong

• (a)
  (1, −1) — (1, −1) does lie on the line: 4(1) − 5 = −1. But (0, −5) and (2, 3) do too, so naming one point is incomplete when option (d) covers all three.
• (b)
  (0, −5) — (0, −5) is the y-intercept (put x = 0), so it is on the line. It is a true point but not the complete answer, since the other two points pass as well.
• (c)
  (2, 3) — (2, 3) satisfies y = 4x − 5, since 8 − 5 = 3. Stopping here misses that (1, −1) and (0, −5) satisfy it too.

A point lies on a graph when its coordinates satisfy the equation: put x in, and the equation must return the point's y.

y = 4x − 5 is a straight line with slope 4 and y-intercept −5. The three points are collinear: from (0, −5) to (1, −1) to (2, 3), y rises by 4 each time x rises by 1.

Key facts

• A point (x₁, y₁) lies on y = mx + c exactly when y₁ = mx₁ + c.
• In y = mx + c, m is the slope and c is the y-intercept, the point (0, c).
• y = 4x − 5 has slope 4 and crosses the y-axis at (0, −5).

Common traps

• Stopping at the first point that works when All the above is on offer
• Swapping the coordinates, putting the point's y in place of x

No directly related past PYQ was found.