SOLUTION: whats the slope of the coordinates M (9,6), N(1,4) and whats the slope perpendicular to it

Question 475578: whats the slope of the coordinates M (9,6), N(1,4) and whats the slope perpendicular to it

Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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

Reduce

So the slope of the line that goes through the points and is

The slope of any line perpendicular to this one will have a slope that is a negative reciprocal of this one. So simply flip the fraction and change the sign to get

So the perpendicular slope is
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Finding the slope

Slope of the line through the points (9, 6) and (1, 4)

Answer: Slope is

the slope perpendicular to it is

now we can find the Equation of a line that passes through M (9,6) and N(1,4)

Solved by pluggable solver: Finding the Equation of a Line

First lets find the slope through the points (,) and (,)

Start with the slope formula (note: (,) is the first point (,) and (,) is the second point (,))

Plug in ,,, (these are the coordinates of given points)

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get

Reduce

So the slope is

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Now let's use the point-slope formula to find the equation of the line:

------Point-Slope Formula------
where is the slope, and (,) is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

Plug in , , and (these values are given)

Distribute

Multiply and to get

Add to both sides to isolate y

Combine like terms and to get (note: if you need help with combining fractions, check out this solver)

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Answer:

So the equation of the line which goes through the points (,) and (,) is:

The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is

Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver )

Graph of through the points (,) and (,)

Notice how the two points lie on the line. This graphically verifies our answer.

so, the line perpendicular to it is

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