Question

Write the standard form of the equation of the line passing through the point (1,3) and perpendicular to the line x-2y=-8.

Answer 1

You need an equation of the form
$$
y=mx+b
$$
The line perpendicular to x-2y=-8 will have a slope that is the negative inverse of this line:

$$
x-2y=-8\\
-2y=-8-x\\
y=(1/2)x+4
$$
Since the slope of this equation is (1/2), the slope of the line perpendicular to it will have slope -2:
$$
y=-2x+b
$$
Since the lines must intersect at point (1,3), set x=1 and y=3 to find b for your perpendicular equation:
$$
3=-2(1)+b\\
b=3+2=5
$$
so the line perpendicular to x-2y=-8 and going through point (1,3) is
$$
y=-2x+5
$$

Make sense?