A straight line can be written using slope-intercept form y = mx + c.\nWhat is the equation of the line with slope 1/3 and y-intercept 5?

Introduction / Context:
This question tests converting between different forms of a line equation. Given a slope and y-intercept, the simplest form is slope-intercept form: y = mx + c. Many multiple-choice options are presented in standard form (Ax + By = C), so the key is to rewrite correctly without sign mistakes.

Given Data / Assumptions:

• Slope m = 1/3.
• y-intercept c = 5 (meaning the line crosses the y-axis at y = 5).
• We must identify the correct equation among the options.

Concept / Approach:
Use y = mx + c. Substitute m = 1/3 and c = 5. Then clear the fraction by multiplying both sides by 3 to convert to integer coefficients. Finally compare with the options.

Step-by-Step Solution:
Start with slope-intercept form: y = mx + c Substitute m = 1/3 and c = 5: y = (1/3)x + 5 Multiply both sides by 3: 3y = x + 15 Rearrange to standard form: x - 3y = -15

Verification / Alternative check:
Check intercept: set x = 0 in x - 3y = -15 => -3y = -15 => y = 5, correct. Check slope quickly: rewrite x - 3y = -15 as 3y = x + 15 => y = (1/3)x + 5, slope is 1/3, correct.

Why Other Options Are Wrong:
x - 3y = 15 gives y-intercept -5, not 5.
x + 3y = 15 or x + 3y = -15 produces a negative slope (-1/3), not 1/3.
3x - y = 15 corresponds to y = 3x - 15, which has slope 3 and wrong intercept.

Common Pitfalls:
Mixing up the sign when moving terms, or incorrectly multiplying by 3 (for example making 3y = x + 5 instead of x + 15). Another mistake is confusing y-intercept with x-intercept.

Final Answer:
x - 3y = -15