[tex]\huge{\boxed{y=\frac{1}{2} x+1}}[/tex]
First, we must find the slope of the graphed line. We can use the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are known points on the line.
Plug in the values. [tex]\frac{4-2}{-1-0}[/tex]
Subtract. [tex]\frac{2}{-1}[/tex]
Simplify. [tex]-2[/tex]
To find the slope of the perpendicular line, we must find the opposite inverse slope. This means we first need to multiply it by [tex]-1[/tex], then we need to swap the numerator and denominator.
[tex]-2*-1=2[/tex]
Now, swap the numerator and denominator. The numerator is [tex]2[/tex], and the denominator is [tex]1[/tex] by default.
[tex]\frac{1}{2}[/tex]
The only answer choice with a slope of [tex]\frac{1}{2}[/tex] is [tex]\boxed{y=\frac{1}{2} x+1}[/tex]
