Find the equation in point slope form of the lines through point p(2,0) that are a) parallel to, and b) perpendicular to the line of x-2y=3.

Parallel:

Perpendicular:

Step-by-step explanation:

Parallel lines have the same slope.

Perpendicular lines have opposite reciprocal slopes.

The point slope form of a line is:

where is a point on the line and 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 because it tells us the slope,m, which is what we need.

Parallel lines will have the same slope, .

Perpendicular lines will have the opposite reciprocal slope: .

So let's put into form by solving for .

Subtract on both sides:

Divide both sides by -2:

Simplify:

or

.

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.

Plug in and :

Now the perpendicular one:

Plug in and :

(1,4) is on graph of f(x)

f(1) = 4

so 1/4 f(x)

1/4 f(1)

1/4. ×4

1

so point for function 1/4. f(x) is (1,1)