If a line crosses the x-axis at x = 4 and the y-axis at y = -3, which of the following is its intercept form equation?

If a line crosses the x-axis at x = 4 and the y-axis at y = -3, which of the following is its intercept form equation?

• A. 4x + 3y = 12
• B. x/4 - y/3 = 1
• C. x/4 + y/3 = 1
• D. x/(-4) - y/3 = 1

Answer: (B)

Intercept form uses x/a + y/b = 1, where a and b are the x- and y-intercepts. Here the line crosses the x-axis at 4 and the y-axis at -3, so a = 4 and b = -3. Plugging those in gives x/4 + y/(-3) = 1, which is x/4 - y/3 = 1. This matches the given intercepts: when y = 0, x/4 = 1, so x = 4; when x = 0, -y/3 = 1, so y = -3. Other forms would imply different intercepts (for example, a sign change would flip the y-intercept to +3, or a negative x-intercept), so they don’t fit the given data.

Intercept form uses x/a + y/b = 1, where a and b are the x- and y-intercepts. Here the line crosses the x-axis at 4 and the y-axis at -3, so a = 4 and b = -3. Plugging those in gives x/4 + y/(-3) = 1, which is x/4 - y/3 = 1. This matches the given intercepts: when y = 0, x/4 = 1, so x = 4; when x = 0, -y/3 = 1, so y = -3. Other forms would imply different intercepts (for example, a sign change would flip the y-intercept to +3, or a negative x-intercept), so they don’t fit the given data.