Question

what is the slope of the line with equation $y - 3 = -\frac{1}{2}(x - 2)$? (image of a coordinate plane with a line passing through (2,3) and (4,2), and multiple - choice options: -2, $-\frac{1}{2}$, $\frac{1}{2}$ (partially visible))

Explanation:

Step1: Recall Point - Slope Form

The point - slope form of a linear equation is given by \(y - y_1=m(x - x_1)\), where \(m\) is the slope of the line and \((x_1,y_1)\) is a point on the line.

Step2: Compare with Given Equation

The given equation is \(y - 3=-\frac{1}{2}(x - 2)\). By comparing this equation with the point - slope form \(y - y_1=m(x - x_1)\), we can see that \(m =-\frac{1}{2}\).

Answer:

\(-\frac{1}{2}\)