SOLUTION: Find the equation of the line that passes through the point (1 ,-8 ) with a slope of 2/5.

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the line that passes through the point (1 ,-8 ) with a slope of 2/5.       Log On


   

Question 1042470: Find the equation of the line that passes through the point (1 ,-8 ) with a slope of 2/5.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the point-slope form, which you should memorize:

y-y%5B1%5D%22%22=%22%22m%28x-x%5B1%5D%29

Plug in 
1 for x1,
-8 for y1, and
2%2F5 for m.

y-%28-8%29%22%22=%22%22expr%282%2F5%29%28x-1%29

Simplify the -(-8) as +8 on the left:

y%2B8%22%22=%22%22expr%282%2F5%29%28x-1%29

Multiply both sides by 5 to clear the fraction on the right.

5%2A%28y%2B8%29%22%22=%22%225%2Aexpr%282%2F5%29%28x-1%29

Distribute the 5 on the left, cancel the 5's on the right:

5y%2B40%29%22%22=%22%22cross%285%29%2Aexpr%282%2Fcross%285%29%29%28x-1%29

5y%2B40%22%22=%22%222%28x-1%29

Next distribute the 2 on the right:

5y%2B40%22%22=%22%222x-2%29

Add -40 to both sides:

5y%2B40-40%22%22=%22%222x-2-40%29

Combine terms:

5y%22%22=%22%222x-42%29

Divide every number (just the numbers) by 5

expr%285%2F5%29y%22%22=%22%22expr%282%2F5%29x-expr%2842%2F5%29

Cancel the 5's on the left.  They don't cancel on the right
so just leave them as they are.

expr%28cross%285%29%2Fcross%285%29%29y%22%22=%22%22expr%282%2F5%29x-expr%2842%2F5%29

y%22%22=%22%22expr%282%2F5%29x-expr%2842%2F5%29

Edwin