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Let line $l_1$ be the graph of $5x + 8y = -9$. Line $l_2$ is perpendicular to line $l_1$ and passes through the point $(10,10)$. If line $l_2$ is the graph of the equation $y=mx +b$, then find $m+b$.



The perpendicular bisector of the line segment $\overline{AB}$ is the line that passes through the midpoint of $\overline{AB}$ and is perpendicular to $\overline{AB}$.
Find the equation of the perpendicular bisector of the line segment joining the points $(1,2)$ and $(7,4).$ Enter your answer in the form "$y = mx + b$."



The lines $3y + 2x = 7$ and $y = mx - 11$ are perpendicular. Find $m.$

 Nov 9, 2017

1) To find a perpendicular line, the slope is the negative reciprocal.

Get the equation into y=mx+b form.


Subtract 5x from both sides.


Divide both sides by 8.


Take the negative reciprocal of m and use it with (10,10) in point-slope form, y-y1=m(x-x1).


Multiply the 8/5 through and add 10 to both sides.



Then, m+b would be 8/5-6. This is 1.6-6, or -5.6.


2) The slope of a line is \(\frac{y_2-y_1}{x_2-x_1}\).

Plug in the points (1,2) and (7,4)


So the slope is 1/3. Now use point-slope form.


Distribute 1/3 and add 2 to both sides.






3) Put 3y+2x=7 into y=mx+b form.


Divide by 3.


The slope of a line perpendicular to another is the negative reciprocal of the first slope.


So 3/2 is the answer to #3.

 Nov 9, 2017

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