Intercept form of a line with x-intercept a and y-intercept b is expressed as which equation?

• A. x/a + y/b = 0
• B. x/a + y/b = 1
• C. ax + by = ab
• D. x^2/a^2 + y^2/b^2 = 1

Answer: (B)

Intercept form uses where the line crosses the axes. If a line meets the x-axis at (a, 0) and the y-axis at (0, b), its equation is x/a + y/b = 1. This works because setting y to 0 gives x/a = 1, so x = a, and setting x to 0 gives y/b = 1, so y = b. The slope comes out as -b/a, matching a line through those intercepts. Other forms would not give those same intercepts (for example, x/a + y/b = 0 would yield an x-intercept of 0, and ax + by = ab effectively swaps the intercepts), and the last option describes a ellipse, not a line.