SOLUTION: A line passing through (�6, �5) and (�1, y) is perpendicular to a line with slope -5/13 . Find the value of y.

Question 111717: A line passing through (�6, �5) and (�1, y) is perpendicular to a line with slope -5/13 . Find the value of y.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
A line passing through (�6, �5) and (�1, y) is perpendicular to a line with slope -5/13 . Find the value of y.

to find the value of , you first need to use the given data that this line is to a line with slope , so you can calculate a slope for your line
we know that if the lines are perpendicular, then :
find for line:

�.this is a slope of a line passing through (�6, �5) and (�1, y)

we can calculate using this formula:

��move to the left
��multiply both sides by
��
��
��,,,,,,,,,,,,,,,,,,

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

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)

Rewrite as

Rewrite as

Distribute

Multiply and to get

Subtract from 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.

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