Answer:
Parallel: [tex]y-0=\frac{1}{2}(x-2)[/tex]
Perpendicular: [tex]y-0=-2(x-2)[/tex]
Step-by-step explanation:
Parallel lines have the same slope.
Perpendicular lines have opposite reciprocal slopes.
The point slope form of a line is:
[tex]y-y_1=m(x-x_1)[/tex]
where [tex](x_1,y_1)[/tex] is a point on the line and [tex]m[/tex] is the slope.
To find the slope we will first have to find the slope of the given line.
We are going to put it into slope-intercept form [tex]y=mx+b[/tex] because it tells us the slope,m, which is what we need.
Parallel lines will have the same slope, [tex]m[/tex].
Perpendicular lines will have the opposite reciprocal slope: [tex]\frac{-1}{m}[/tex].
So let's put [tex]x-2y=3[/tex] into [tex]y=mx+b[/tex] form by solving for [tex]y[/tex].
[tex]x-2y=3[/tex]
Subtract [tex]x[/tex] on both sides:
[tex]-2y=-x+3[/tex]
Divide both sides by -2:
[tex]y=\frac{-x}{-2}+\frac{3}{-2}[/tex]
Simplify:
[tex]y=\frac{x}{2}-\frac{3}{2}[/tex]
or
[tex]y=\frac{1}{2}x-\frac{3}{2}[/tex].
So the slope is 1/2 for the given equation.
Our parallel line will also have slope 1/2.
Our perpendicular line will have slope -2.
Let's move onto finding these equations starting with the parallel one.
[tex]y-y_1=m(x-x_1)[/tex]
Plug in [tex]m=\frac{1}{2}[/tex] and [tex](2,0)[/tex]:
[tex]y-0=\frac{1}{2}(x-2)[/tex]
Now the perpendicular one:
[tex]y-y_1=m(x-x_1)[/tex]
Plug in [tex]m=-2[/tex] and [tex](2,0)[/tex]:
[tex]y-0=-2(x-2)[/tex]
