Question

what is the slope of the line with equation $y - 3 = -\frac{1}{2}(x - 2)$?
options: $-2$, $\frac{1}{2}$ (and the image of the coordinate plane with the line and points (2,3), (4,2))

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 \(m =-\frac{1}{2}\). (We can also verify this using the two points \((2,3)\) and \((4,2)\) from the graph. The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 2,y_1=3,x_2 = 4,y_2 = 2\), we get \(m=\frac{2 - 3}{4 - 2}=\frac{-1}{2}=-\frac{1}{2}\))

Answer:

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