SOLUTION: I have two questions on the equations of lines. 1)Write an equation of a line passing through the points (-3,5) and (2,-7) 2) Write an equation of the line perpendicular to

Question 275270: I have two questions on the equations of lines.
1)Write an equation of a line passing through the points (-3,5) and (2,-7)

2) Write an equation of the line perpendicular to the line 2x-4y=7 and passing through (2,-5)
I am slightly perplexed, thanks in advance.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

First let's find the slope of the line through the points

and

Note:

is the first point

. So this means that and .
Also,

is the second point

. So this means that and .

Start with the slope formula.

Plug in , , , and

Subtract from to get

Subtract from to get

So the slope of the line that goes through the points

and

is

Now let's use the point slope formula:

Start with the point slope formula

Plug in , , and

Rewrite as

Distribute

Multiply

Add 5 to both sides.

Combine like terms. note: If you need help with fractions, check out this solver.

So the equation that goes through the points

and

is

======================================

# 2

Start with the given equation.

Subtract from both sides.

Rearrange the terms.

Divide both sides by to isolate y.

Break up the fraction.

Reduce.

So the slope of and is

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 (2,-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

Subtract from both sides to isolate y

Combine like terms

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 (,)

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