SOLUTION: I need help finding an equation of a line passing through the points (4,9) and (3,-2) and then writing the equation in the form Ax+By=C. I have tried to understand it but still hav

Algebra ->  Linear-equations -> SOLUTION: I need help finding an equation of a line passing through the points (4,9) and (3,-2) and then writing the equation in the form Ax+By=C. I have tried to understand it but still hav      Log On


   

Question 600678: I need help finding an equation of a line passing through the points (4,9) and (3,-2) and then writing the equation in the form Ax+By=C. I have tried to understand it but still have trouble. Can you please help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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


Note: is the first point . So this means that x%5B1%5D=4 and y%5B1%5D=9.
Also, is the second point . So this means that x%5B2%5D=3 and y%5B2%5D=-2.


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


m=%28-2-9%29%2F%283-4%29 Plug in y%5B2%5D=-2, y%5B1%5D=9, x%5B2%5D=3, and x%5B1%5D=4


m=%28-11%29%2F%283-4%29 Subtract 9 from -2 to get -11


m=%28-11%29%2F%28-1%29 Subtract 4 from 3 to get -1


m=11 Reduce


So the slope of the line that goes through the points and is m=11


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-9=11%28x-4%29 Plug in m=11, x%5B1%5D=4, and y%5B1%5D=9


y-9=11x%2B11%28-4%29 Distribute


y-9=11x-44 Multiply


y-9%2B9=11x-44%2B9 Add 9 to both sides


y=11x-35 Combine like terms.


y-11x=11x-35-11x Subtract 11x from both sides


y-11x=-35 Combine like terms.


-11x%2By=-35 Rearrange the terms.


11x-y=35 Multiply EVERY term by -1 to make the leading coefficient (the x coefficient) positive.


So the answer is 11x-y=35