SOLUTION: I am in need of a simplified way of doing equation of a line. The question being find an equation of the line containing the given pair of paints (-5, -2) and (-3, -1). The equatio

Algebra ->  Linear-equations -> SOLUTION: I am in need of a simplified way of doing equation of a line. The question being find an equation of the line containing the given pair of paints (-5, -2) and (-3, -1). The equatio      Log On


   

Question 317008: I am in need of a simplified way of doing equation of a line. The question being find an equation of the line containing the given pair of paints (-5, -2) and (-3, -1). The equation of the line in slope interecept form is y= ___
Then simplify the naswer. Use integer or fractions for nay numbers in the expression. I know that the formula is y = mx + b but just cannot make it work in my head. Can you 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=-5 and y%5B1%5D=-2.
Also, is the second point . So this means that x%5B2%5D=-3 and y%5B2%5D=-1.


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


m=%28-1--2%29%2F%28-3--5%29 Plug in y%5B2%5D=-1, y%5B1%5D=-2, x%5B2%5D=-3, and x%5B1%5D=-5


m=%281%29%2F%28-3--5%29 Subtract -2 from -1 to get 1


m=%281%29%2F%282%29 Subtract -5 from -3 to get 2


So the slope of the line that goes through the points and is m=1%2F2


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=%281%2F2%29%28x--5%29 Plug in m=1%2F2, x%5B1%5D=-5, and y%5B1%5D=-2


y--2=%281%2F2%29%28x%2B5%29 Rewrite x--5 as x%2B5


y%2B2=%281%2F2%29%28x%2B5%29 Rewrite y--2 as y%2B2


y%2B2=%281%2F2%29x%2B%281%2F2%29%285%29 Distribute


y%2B2=%281%2F2%29x%2B5%2F2 Multiply


y=%281%2F2%29x%2B5%2F2-2 Subtract 2 from both sides.


y=%281%2F2%29x%2B1%2F2 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation that goes through the points and is y=%281%2F2%29x%2B1%2F2