Question

Multiple Choice Which of the following is an equation of the line through \((-3,4)\) with slope 1\(/ 2 ?\) (A) \(y-4=\frac{1}{2}(x+3) \quad\) (B) \(y+3=\frac{1}{2}(x-4)\) \(\begin{array}{ll}{(\mathrm{C}) y-4=-2(x+3)} & {(\text { D) } y-4=2(x+3)} \\\ {\text { (E) } y+3=2(x-4)}\end{array}\)

Short answer

The equation of the line is \(y-4=\frac{1}{2}(x+3)\), so the correct choice is (A)

Step-by-step solution

Identify the Points and Slope

From the problem, identify that the slope (m) is 1/2, and the point (x1, y1) the line passes through is (-3, 4).

Use the Point-Slope Form of a Line

Replace m, x1, y1 with the values from the given problem in the point-slope equation. This results in: \(y-4=\frac{1}{2}(x+3)\).

Identify the Correct Choice

Compare the derived equation from step 2 with the provided choices and select the one that matches. The equation \(y-4=\frac{1}{2}(x+3)\) is option (A). So, choice (A) is the correct answer