Which equation is in point-slope form with slope 3 through (4, 2)?

• A. y - 2 = 3(x - 4)
• B. y = 3x + 14
• C. y - 4 = 3(x - 2)
• D. y = 3x - 4

Answer: (A)

Point-slope form uses a known point and the slope: y - y1 = m(x - x1). With slope 3 and the point (4, 2), plug in y1 = 2, x1 = 4, m = 3 to get y - 2 = 3(x - 4). This is exactly the point-slope form for a line through (4, 2) with slope 3. If you expand, you’d get y = 3x - 10, but the expression shown is already in the requested form. The other expressions don’t fit because they either use a different point or are written in a different form, e.g., y = 3x + 14 would not pass through (4, 2); y - 4 = 3(x - 2) would go through (2, 4); and y = 3x - 4 would give y = 8 when x = 4, not 2.