Question

if the points (3,r) and (r,-1) lie on a line with slope (-3/4) what is the value of r?

Answer 1

okay so we have got 2 points...
Let's call them A and B. where A(3,r) and B(r,-1).

Answer 2

we want to find the value of r, so let's tke those points and find the equation of the line that goes through those points.

Answer 3

We have the slope, so it would be optimal to do this exercise with the point-slope formula and taking arbitrary A or B. Do you follow?

Answer 4

I understand all except the last response, can you explain what arbitrary means?

Answer 5

arbitrary means basically "any you want" so you can choose any of those points to apply the point-slope formula.

Answer 6

so where would we go from there?

Answer 7

Now, we have two points, i'll pick point A(3,r) and use the point slope formula:
\[y-y _{1}=m(x-x_{1})\]
where m is the slope and x1, y1 the point's coordinates.
I'll use that for A(3,r), ending up with:
\[y-r=-\frac{ 3 }{ 4 }(x-3)\]
I'll apply distributive to get rid if the -3/4:
\[y-r=-\frac{ 3x }{ 4 }+\frac{ 9 }{ 4 }\]
continuing let's add "r" to both sides and use common denominator:
\[y=\frac{ -3x+9+4r }{ 4 }\]
multiplying both sides by 4 we get:
\[4y=-3x+9+4r\]
So now we found an equation that can help us find r, and we know that point B belongs to this line, so we can replace x and y with the coordinates of B:
\[-4=-3r+9+4r\]
operating a little, we get:
\[(4-3)r=9-4\]
and our final answer is:
\[r=5\]
Not hard, was it.
Now try doing it but picking B first.

Answer 8

That makes sense, thank you!
but I don't think i did point b right

r+1=(-3/4)(3-r)
r+1=-9/4-3/4r
1/4r=-13/4
r=-13

Answer 9

oh, you have to write the point-slope equation for just one point, simplify and then replace the values of the points.

Answer 10

so is the value of r 5 or -13?

Answer 11

5 right? i think i see where i went wrong

Answer 12

yeah i set the equation up wrong, thank you so much!!!

Answer 13

No problem, I love helping people.