Question

consider the linear function graphed on the coordinate plane below. part a what is the slope of the line? (a) part b which equation correctly represents the line in point - slope form? a $y=\frac{1}{2}(x - 3)+2$ a $y=-\frac{1}{2}(x - 3)+2$ c $y=-\frac{1}{2}(x + 3)-2$ d $y=2(x + 3)-2$

Explanation:

Step1: Recall point - slope form formula

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. We know from part A that $m =-\frac{1}{2}$, and we can use the point $(3,2)$ (we could also use $(-1,4)$).

Step2: Substitute values into formula

Substitute $m =-\frac{1}{2}$, $x_1 = 3$, and $y_1 = 2$ into the point - slope form. We get $y-2=-\frac{1}{2}(x - 3)$, which can be rewritten as $y=-\frac{1}{2}(x - 3)+2$.

Answer:

B. $y =-\frac{1}{2}(x - 3)+2$