If a line has slope 3 and passes through (4, -2), which equation is the point-slope form?

• A. 3x + y = 1
• B. y - (-2) = 3(x - 4)
• C. 2y - x = 4
• D. y = 3x + b

Answer: (B)

The concept here is that a line in point-slope form uses a known point on the line and the slope: y − y1 = m(x − x1). With a slope of 3 and the point (4, −2), you plug in m = 3, x1 = 4, y1 = −2 to get y − (−2) = 3(x − 4). This simplifies to y + 2 = 3x − 12, and the same holds if you leave it in the exact point-slope way. This form directly encodes both the slope and a specific point on the line, which is why it matches the requirement. The other forms are not in this structure: one is a slope-intercept form with an unknown b, one is a standard form that doesn’t reflect the given point in the (x − x1) part, and another rearranges to a different slope or presentation.