The line y = mx + 5 passes through (1,8). Find m.

Correct — C. A point lies on a line when its coordinates satisfy the equation.

Put x = 1 and y = 8 into y = mx + 5:
8 = m × 1 + 5
Subtract 5 from both sides: m = 8 − 5 = 3 → option (c)

Check: y = 3x + 5 at x = 1 gives 3 + 5 = 8 ✓

Why the others are wrong

• (a)
  5 — 5 is the y-intercept, not the slope. With m = 5 the line gives y = 5 + 5 = 10 at x = 1, so it misses (1, 8).
• (b)
  4 — m = 4 gives y = 4 + 5 = 9 at x = 1. That line passes through (1, 9), one unit above the given point.
• (d)
  2 — m = 2 gives y = 2 + 5 = 7 at x = 1. That line passes through (1, 7), one unit below the given point.

In y = mx + c, m is the slope — the rise in y for each unit step in x — and c is the y-intercept, where the line crosses the y-axis.

Any point on the line makes the equation true. Substituting the point's x and y leaves one unknown, here m.

Read as a slope: the line passes through (0, 5) and (1, 8), so y rises 3 while x rises 1 — slope 3.

Key facts

• In y = mx + c, m is the slope and c is the y-intercept.
• The line y = mx + 5 passes through (0, 5) whatever the value of m.
• Slope between two points = (y₂ − y₁) ÷ (x₂ − x₁): (8 − 5) ÷ (1 − 0) = 3.

Common traps

• Reading the constant 5 as the slope, when in y = mx + 5 it is where the line crosses the y-axis.
• Substituting the point the wrong way round, x = 8 and y = 1, which gives 1 = 8m + 5 and m = −1⁄2.

No directly related past PYQ was found.