Write each equation in point-slope form.
Slope: $m=\frac{1}{3}$; Point: $(-2,4)$

• A. $y-4=\frac{1}{3}(x-2)$
• B. $y-4=\frac{1}{3}(x+2)$
• C. $y-\frac{1}{3}=4(x+2)$
• D. $y-\frac{1}{3}=4(x-2)$

Answer: (B)

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 slope \(m\) and the point \((x_1, y_1)\) from the problem. Here, the slope \(m = \frac{1}{3}\) and the point is \((-2, 4)\).
3. Substitute the slope and the coordinates of the point into the point-slope formula: \(y - 4 = \frac{1}{3}(x - (-2))\).
4. Simplify the expression inside the parentheses by changing the subtraction of a negative number to addition: \(y - 4 = \frac{1}{3}(x + 2)\).
5. This is the equation in point-slope form using the given slope and point.