SOLUTION: The question is: Find an equation of the line that has the same y-intercept as the line x-3y=6 and contains the points (5,1). I though I needed to find the y-intercept first, wh

Algebra ->  Linear-equations -> SOLUTION: The question is: Find an equation of the line that has the same y-intercept as the line x-3y=6 and contains the points (5,1). I though I needed to find the y-intercept first, wh      Log On


   

Question 195139: The question is: Find an equation of the line that has the same y-intercept as the line x-3y=6 and contains the points (5,1).
I though I needed to find the y-intercept first, which I believe is to be (0,3), but I'm not sure what I doing with the (5,1). I know how to enter the points into an equation. Just not sure what the steps are to solving this question.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x-3y=6 Start with the given equation.


-3y=6-x Subtract x from both sides.


-3y=-x%2B6 Rearrange the terms.


y=%28-x%2B6%29%2F%28-3%29 Divide both sides by -3 to isolate y.


y=%28%28-1%29%2F%28-3%29%29x%2B%286%29%2F%28-3%29 Break up the fraction.


y=%281%2F3%29x-2 Reduce.


So the equation y=%281%2F3%29x-2 is now in slope intercept form y=mx%2Bb where the slope is m=1%2F3 and the y-intercept is b=-2

So the y-intercept is the point (0, -2)


So all we need to do is find the equation of the line through (0,-2) and (5,1)





First let's find the slope of the line through the points and


Note: is the first point and is the second point .


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%281--2%29%2F%285-0%29 Plug in y%5B2%5D=1, y%5B1%5D=-2, x%5B2%5D=5, and x%5B1%5D=0


m=%283%29%2F%285-0%29 Subtract -2 from 1 to get 3


m=%283%29%2F%285%29 Subtract 0 from 5 to get 5


So the slope of the line that goes through the points and is m=3%2F5


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y--2=%283%2F5%29%28x-0%29 Plug in m=3%2F5, x%5B1%5D=0, and y%5B1%5D=-2


y%2B2=%283%2F5%29%28x-0%29 Rewrite y--2 as y%2B2


y%2B2=%283%2F5%29x%2B%283%2F5%29%28-0%29 Distribute


y%2B2=%283%2F5%29x%2B0 Multiply


y=%283%2F5%29x%2B0-2 Subtract 2 from both sides.


y=%283%2F5%29x-2 Combine like terms.


So the equation that goes through the points and is y=%283%2F5%29x-2