Which equation is in point-slope form with slope -2 through point (3, 5)?

• A. y - 5 = -2(x - 3)
• B. y - 5 = -2x - 6
• C. y = -2(x - 3) - 5
• D. y + 5 = -2(x - 3)

Answer: (A)

In point-slope form, a line through a known point (x1, y1) with slope m is written as y - y1 = m(x - x1). Here, m is -2 and the point is (3, 5), so the equation should be y - 5 = -2(x - 3). This directly encodes both the slope and the exact point the line passes through.

That structure is what makes it the correct form. The other expressions either don’t keep the left side as y - y1 or don’t place the point inside the parentheses in the required way, so they don’t represent the line that passes through (3, 5) with slope -2. For example, expanding or rearranging can give lines like y = -2x + 11, y = -2x + 1, or y = -2x - 1, which have the same slope but pass through different points.