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

Question

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

1. A. 5
2. B. 4
3. C. 3 (Correct answer)
4. D. 2

Correct Answer

Option C — 3

Detailed Solution & Explanation

The correct answer is 3.

Key Points

• The line y = mx + 5 passes through (1, 8), so substitute: 8 = m(1) + 5 → m = 8 − 5 = 3.
• To find a slope from a known point, plug the coordinates into the line equation and solve for m — one substitution settles it.

Additional Information

• y = mx + c is the slope-intercept form: m is the slope and c the y-intercept. A point lying on the line must satisfy the equation, which is what allows m to be recovered.
• Substituting (1, 8): 8 = m(1) + 5, so m = 3. The line is y = 3x + 5, cutting the y-axis at (0, 5).
• A slope of 3 means y rises 3 units for every 1 unit of x. Positive slope rises left to right, negative falls, zero is horizontal, and a vertical line has undefined slope.
• Related forms worth carrying into the exam: the two-point slope m = (y₂ − y₁)/(x₂ − x₁); parallel lines share a slope; perpendicular slopes multiply to −1.