A line with slope 3 passing through (0, -2) has equation?

• A. y = -3x - 2
• B. y = 3x + 2
• C. y = 3x - 2
• D. y = x - 2

Answer: (C)

The line’s equation in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Since the slope is 3, m = 3. It passes through (0, -2), so when x = 0, y = -2, which gives b = -2. Therefore the equation is y = 3x - 2.

You can check by plugging in x = 0 to get y = -2, and by noting that increasing x by 1 makes y increase by 3, so at x = 1 the line gives y = 1, which matches y = 3(1) - 2. Choices with a different slope or a different intercept wouldn’t pass through (0, -2) or wouldn’t have slope 3, so they don’t fit.