Which expression represents the slope-intercept form of a line through (0, -1) with slope -3?

Which expression represents the slope-intercept form of a line through (0, -1) with slope -3?

• A. y = 3x - 1
• B. y = -3x + 1
• C. y = 3x + 1
• D. y = -3x - 1

Answer: (D)

In slope-intercept form, a line is written as y = mx + b, where m is the slope and b is the y-intercept. The line passes through (0, -1), so its y-intercept is -1. The given slope is -3, so m = -3 and b = -1. Putting these together gives y = -3x - 1. This also checks out when x = 0: y = -1, matching the given point. The other expressions would either have the wrong slope or the wrong intercept, so they don’t represent this line.

In slope-intercept form, a line is written as y = mx + b, where m is the slope and b is the y-intercept. The line passes through (0, -1), so its y-intercept is -1. The given slope is -3, so m = -3 and b = -1. Putting these together gives y = -3x - 1. This also checks out when x = 0: y = -1, matching the given point. The other expressions would either have the wrong slope or the wrong intercept, so they don’t represent this line.