Question

1.Write the equation of a line through C that is parallel to AB.
2. Write the equation of a line through B that is perpendicular to AC.
Please explain how to do this and help me solve it.

Answer 1

If one line is parallel to another, we know that their slopes are the same.

If they are perpendicular, when you multiply their slopes, it equals -1. That is:
(slope of line)*(slope of perpendicular line) = -1

After we have the slopes, we just pick a y intercept (b) and plug it into y=mx+b
where m is the slope.

If you want it to go through a specific point, we can use the point-slope form:
\[y-y_o = m(x-x_o)\]
with the point being:
\[(x_o,y_o)\]

Answer 2

Does that make sense?

Answer 3

:/ no, im sorry i have been out of school for a year so i forgot a lot of stuff and im having a hard time starting back up.

Answer 4

Ok, do you know how to find the slope of a line?

Answer 5

yeah

Answer 6

Let's do question 1, then. Find the slope of line AB

Answer 7

Ok, if the slope of AB is 3/4, a line that is PARALLEL to AB will have the exact same slope.

Now, we need this line to also go through point C. What are the coordinates of point C?

Answer 8

5,-1

Answer 9

Ok, since we want the line to go through this point, we'll use the point-slope form:
\[y-y_o = m(x-x_o)\]

When we put in the information we know (the slope, and the coordinates of the point we want the line to go through), we get:

\[y-(-1)=\frac{3}{4}(x-5)\]
\[y+1=\frac{3}{4}(x-5)\]

Then we just solve for y.

Answer 10

what is the little circle by the y mean?

Answer 11

It means that it's the y coordinate of the point you want the line to go through.

Answer 12

It's the coordinates for C, in this case, since we want the line to go through C.

C = (5,-1)
So:
\[x_o = 5\]
\[y_o = -1\]

Answer 13

I'm only confused because it doesn't show that in my book.

Answer 14

If you look for "point slope form," it should have that equation (the subscripts make be different, but it means the same thing)

Answer 15

ok i looked it up in the back of my book the point-slope form: