Option c: [tex]y=-\frac{1}{2} x-2[/tex] is the equation of the line
Explanation:
The equation of line EF is given by [tex]y=-\frac{1}{2}x+6[/tex]
To determine the equation of line in slope intercept form is given by [tex]y=m x+c[/tex] where m is the slope.
From the above equation, the slope of the equation is [tex]m=-\frac{1}{2}[/tex]
Let us substitute the slope in the formula [tex]y=m x+c[/tex]
Thus, the new equation is
[tex]y=-\frac{1}{2} x+c[/tex]
Also, it contains the point (0,-2)
Substituting the point in the equation [tex]y=-\frac{1}{2} x+c[/tex], we get,
[tex]\begin{aligned}&-2=-\frac{1}{2}(0)+c\\&-2=0+c\\&-2=c\end{aligned}[/tex]
Thus, substituting the value of c in the equation [tex]y=-\frac{1}{2} x+c[/tex], we have,
[tex]y=-\frac{1}{2} x-2[/tex]
Thus, the equation of line parallel to the line EF in slope intercept form is [tex]y=-\frac{1}{2} x-2[/tex]
Hence, Option c is the correct answer.
