SOLUTION: (1,5) and (3,13) a) list 2 equations for parellel lines b) find the eqaution of the perpendicular line c) graph the perpindicular line

Question 387806: (1,5) and (3,13)

a) list 2 equations for parellel lines
b) find the eqaution of the perpendicular line
c) graph the perpindicular line
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
and are

since the slope of the line is ,
and the slope of the line is ,
these lines are parallel since a parallel line has an identical slope.
intercept points:
intercept is found by setting to :
becomes ..... that means that
in your case and intercept
point is (-2.5,0)
intercept is found by setting to : the equation becomes , and therefore , so intercept is
point is (0,5)
Slope is .

For the perpendicular line, you have to find the slope. The reference slope is , and, for the perpendicular slope, you will flip this slope and change the sign. Then the slope is

So now you can do the point-slope form.
point is (0,5), and

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line

Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of , you can find the perpendicular slope by this formula:

where is the perpendicular slope

So plug in the given slope to find the perpendicular slope

When you divide fractions, you multiply the first fraction (which is really ) by the reciprocal of the second

Multiply the fractions.

So the perpendicular slope is

So now we know the slope of the unknown line is (its the negative reciprocal of from the line ). Also since the unknown line goes through (0,5), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

where m is the slope and (,) is the given point

Plug in , , and

Distribute

Multiply

Add to both sides to isolate y

Make into equivalent fractions with equal denominators

Combine the fractions

Reduce any fractions

So the equation of the line that is perpendicular to and goes through (,) is

So here are the graphs of the equations and

graph of the given equation (red) and graph of the line (green) that is perpendicular to the given graph and goes through (,)

so, the line is perpendicular to given line and to its parallel line

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