SOLUTION: Find the value of x or y so that the line passing through the two points has the given slope. (-2,8),(x,4); m=4/5 Please help me out, I just cannot seem figure out how to

Algebra ->  Linear-equations -> SOLUTION: Find the value of x or y so that the line passing through the two points has the given slope. (-2,8),(x,4); m=4/5 Please help me out, I just cannot seem figure out how to      Log On


   

Question 207179This question is from textbook Georgia High School Mathematics
: Find the value of x or y so that the line passing through the two points has the given slope.

(-2,8),(x,4); m=4/5

Please help me out, I just cannot seem figure out how to solve this
Any help would be appreciated
thank you very much This question is from textbook Georgia High School Mathematics

Found 2 solutions by Earlsdon, mickclns:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First, recall the formula for the slope, m, of a line when you are given two points on that line:
m+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
The two given points are: (-2,8) and (x,4) and these are the (x%5B1%5D,y%5B1%5D) and (x%5B2%5D,y%5B2%5D) so that:
x%5B1%5D+=+-2, y%5B1%5D+=+8, x%5B2%5D+=+x, and y%5B2%5D+=+4, and m+=+4%2F5 is given.
Make the the appropriate substitutions into the formula for the slope:
4%2F5+=+%284-8%29%2F%28x-%28-2%29%29 Simplify.
4%2F5+=+%28-4%29%2F%28x%2B2%29 Multiply both sides by 5%2F4.
1+=+-5%2F%28x%2B2%29 Multiply both sides by (x+2)
x%2B2+=+-5 Subtract 2 from both sides.
highlight%28x+=+-7%29
Check:
m+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m+=+%284-8%29%2F%28-7-%28-2%29%29
m+=+%28-4%29%2F%28-5%29
m+=+4%2F5

Answer by mickclns(59) About Me  (Show Source):
You can put this solution on YOUR website!
slope is rise over run, that is, (change in y) / (change in x)
In this case change in y doesn't have to be 4 and change in x doesn't have to be 5, just the ratio or fraction has to be the same.
 
In this case, going from the second point to the first (doesn't matter whether 1st to 2nd or 2nd to 1st, BUT it has to be the same direction for both x and y), rise over run is:
%288-4%29%2F%28-2+-+x%29=4%2F5%29 simplifying 8-4
4%2F%28-2+-+x%29=4%2F5 dividing both sides by 4 (makes equation less complicated and the numbers smaller)
1%2F%28-2+-+x%29=1%2F5 cross multiplying or, equivalently, multiplying both sides by 5 and (-2-x))
5=-2+-+x adding 2 to both sides
7+=+-x multiplying both sides by -1
x+=+-7