SOLUTION: Find the equation of the line through the y-intercept of y = x^4 – 3x^5 – 8 + x^2 and the x-intercept of y = 2x – 18. If anyone can explain how to do this that would be awesome! I

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the line through the y-intercept of y = x^4 – 3x^5 – 8 + x^2 and the x-intercept of y = 2x – 18. If anyone can explain how to do this that would be awesome! I      Log On


   



Question 685360: Find the equation of the line through the y-intercept of y = x^4 – 3x^5 – 8 + x^2 and the x-intercept of y = 2x – 18.
If anyone can explain how to do this that would be awesome! I'm so confused. Thanks!

Found 2 solutions by Edwin McCravy, josmiceli:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
To find the y intercept of y = x^4 – 3x^5 – 8 + x^2, substitute x=0 and
solve for y

y = 0^4 – 3(0)^5 – 8 + (0)^2 
y = 0 - 0 - 8 + 0 =
y = -8

So the y intercept of that graph is (x,y) = (0,-8)

To find the y intercept of y = 2x – 18, substitute y=0 and
solve for x

  y = 2x – 18
  0 = 2x - 18
-2x = -18
  x = 9

So the x intercept of that graph is (x,y) = (9,0)

So now the problem becomes:

Find the equation of the line which passes through the
two points (0,-8) and (9,0)

The slope is given by the formula:

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m = %280-%28-8%29%29%2F%289-0%29

m = 8%2F9


So the y intercept of that graph is (x,y) = (0,-8),

so b = -8.

We can just use y = mx + b and get

y = 8%2F9x - 8

Edwin


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Find the y-intercept of +y+=+x%5E4+%96+3x%5E5+%96+8+%2B+x%5E2+
Important rule:
The y-intercept occurs where +x+=+0+
Note that +y+ really is a function of +x+, then
there is only ONE y-intercept
--------------------------
+y%280%29+=+0%5E4+%96+3%2A0%5E5+%96+8+%2B+0%5E2+
+y%280%29+=+-8+
It is important to note that this intercept is
the point (0,-8)
--------------
Now find the x-intercept of +y+=+2x+%96+18+
The x-intercept occurs where ++y+=+0+
+0+=+2x+-+18+
+2x+=+18+
+x+=+9+
This is the x-intercept. Note that a valid function
can have MANY x-intercepts, but a straight line
like this one has only ONE x-intercept.
This intercept is at the point (9,0)
----------------------------
Now you need to find the equation that goes
through these points (0,-8) and (9,0)
Use the general point-slope formula.
+%28+y+-+%28-8%29+%29+%2F+%28+x+-+0+%29+=+%28+0+-%28-8%29+%29+%2F+%28+9+-+0%29+
+%28+y+%2B+8+%29+%2F+x+=+8+%2F+9+
Multiply both sides by +9x+
+9%2A%28+y+%2B+8+%29+=+8x+
+9y+%2B+72+=+8x+
+9y+=+8x+-+72+
+y+=+%288%2F9%29%2Ax+-+8+
----------------
check answer:
Does it go through (0,-8) ?
+y+=+%288%2F9%29%2Ax+-+8+
+-8+=+%288%2F9%29%2A0+-+8+
+-8+=+-8+
----------
Does it go through (9,0) ?
+y+=+%288%2F9%29%2Ax+-+8+
+0+=+%288%2F9%29%2A9+-+8+
+0+=+8+-+8+
+0+=+0+
OK