Write each equation in point-slope form.
Slope: $m=4$; Point: $(1,-2)$

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

Answer: (D)

Verified step by step guidance

1. Recall the point-slope form of a linear equation, which is given by the formula: \(y - y_1 = m(x - x_1)\), where \(m\) is the slope and \((x_1, y_1)\) is a point on the line.
2. Identify the given slope \(m\) and the coordinates of the given point. Here, the slope \(m = 4\) and the point is \((1, -2)\).
3. Substitute the slope \(m = 4\) into the formula, replacing \(m\) with 4: \(y - y_1 = 4(x - x_1)\).
4. Substitute the coordinates of the point \((1, -2)\) into the formula, replacing \(x_1\) with 1 and \(y_1\) with -2: \(y - (-2) = 4(x - 1)\).
5. Simplify the expression \(y - (-2)\) to \(y + 2\), so the equation in point-slope form is \(y + 2 = 4(x - 1)\).