Answer:
[tex]y=-\frac{1}{2}x+8[/tex]
Step-by-step explanation:
The slope of a line perpendicular to another line always has the opposite of the reciprocal of the lines slope. So, we can start the equation with [tex]y=-\frac{1}{2}x+b[/tex] with b being the y-intercept. To find the y-intercept, we can plug the values of a point that the line goes through into the equation. In this case, it passes through (4,6), so [tex]6=-\frac{1}{2}(4)+b[/tex]. Solve this equation to find b. [tex]6=-2+b[/tex], [tex]8=b[/tex]. So, we are left with [tex]y=-\frac{1}{2}x+8[/tex].
