Question

PLS HELP

Answer 1

Option c: $y=-\frac{1}{2} x-2$ is the equation of the line

Explanation:

The equation of line EF is given by $y=-\frac{1}{2}x+6$

To determine the equation of line in slope intercept form is given by $y=m x+c$ where m is the slope.

From the above equation, the slope of the equation is $m=-\frac{1}{2}$

Let us substitute the slope in the formula $y=m x+c$

Thus, the new equation is

$y=-\frac{1}{2} x+c$

Also, it contains the point (0,-2)

Substituting the point in the equation $y=-\frac{1}{2} x+c$, we get,

$\begin{aligned}&-2=-\frac{1}{2}(0)+c\\&-2=0+c\\&-2=c\end{aligned}$

Thus, substituting the value of c in the equation $y=-\frac{1}{2} x+c$, we have,

$y=-\frac{1}{2} x-2$

Thus, the equation of line parallel to the line EF in slope intercept form is $y=-\frac{1}{2} x-2$

Hence, Option c is the correct answer.