I don't even know to to start on this problem. It doesn't even give you any coordinates at all so how am I suppose to find the equation for this line?
Well the equation of a line in this case can be given by $\displaystyle y = mx+c$
They have told you that $\displaystyle m= 4$ so $\displaystyle y = 4x+c$
They have also told you the line shares a point with the parabola. This point is $\displaystyle (2, 2^2) = (2,4)$ so
$\displaystyle 4 = 4\times 2+c$
Now solve for $\displaystyle c$ and your done.
Use the form $\displaystyle y=mx+b$
m is slope
b is y intercept
m=4 (given)
Put in the equation:
$\displaystyle y=4x+b$
We are given in the graph a point x=2 there is an interception with the graph $\displaystyle y=x^2$
so $\displaystyle y=(2)^2$ or $\displaystyle y=4$ at that point.
Now you know the point (2,4) is on the graph.
put in 2 for x and 4 for y in the $\displaystyle y=4x+b$ and solve for b:
$\displaystyle y=mx+b$
$\displaystyle 4=4*2+b$
$\displaystyle b=1/2$
now you are done!
$\displaystyle y=4x+.5$
also another way to get
$\displaystyle y = mx+c$
is to use the point slope form
$\displaystyle y-y_1 = m(x - x_1)$
so using point x = 2 and since y=2^2 = 4 with have the point (2,4)
then
$\displaystyle y-4 = 4(x-2) $
$\displaystyle y = 4x - 8 +4$
$\displaystyle y = 4x -4$
Thank you so much for your help guys I really appreciate it. Now I am stuck on this problem. How would I find out the slope of it? I already plugged in the x and y intercepts it gave me into the equation y = x^2 + 1 and got the coordinate (square root of 7, 5). I'm thinking the top of the triangle is 10 and the right side might be 1 but I'm not quite sure. So that makes it a rise over run of 1/10. Is that the correct slope?
you have to do the rise/run based on the 2 points
first find the (x,y) of the 2 intersecting points
then use $\displaystyle m = \frac{y-y_1}{x-x_1}$ for the slope
as you have found
$\displaystyle Q(2,5)$ and $\displaystyle P(\sqrt{7},8)$
then
$\displaystyle m = \frac{8-5}{\sqrt{7}-2}$
then just simplify
I got $\displaystyle m=\sqrt{7} + 2 $ but double check this