SOLUTION: Find an equation of the line containing the given points (-7,-8)and (-4,-6)

Algebra ->  Linear-equations -> SOLUTION: Find an equation of the line containing the given points (-7,-8)and (-4,-6)      Log On


   

Question 694421: Find an equation of the line containing the given points (-7,-8)and (-4,-6)
Found 2 solutions by jim_thompson5910, Ave:
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=-7 and y%5B1%5D=-8.
Also, is the second point . So this means that x%5B2%5D=-4 and y%5B2%5D=-6.


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


m=%28-6--8%29%2F%28-4--7%29 Plug in y%5B2%5D=-6, y%5B1%5D=-8, x%5B2%5D=-4, and x%5B1%5D=-7


m=%282%29%2F%28-4--7%29 Subtract -8 from -6 to get 2


m=%282%29%2F%283%29 Subtract -7 from -4 to get 3


So the slope of the line that goes through the points and is m=2%2F3


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--8=%282%2F3%29%28x--7%29 Plug in m=2%2F3, x%5B1%5D=-7, and y%5B1%5D=-8


y--8=%282%2F3%29%28x%2B7%29 Rewrite x--7 as x%2B7


y%2B8=%282%2F3%29%28x%2B7%29 Rewrite y--8 as y%2B8


y%2B8=%282%2F3%29x%2B%282%2F3%29%287%29 Distribute


y%2B8=%282%2F3%29x%2B14%2F3 Multiply


y=%282%2F3%29x%2B14%2F3-8 Subtract 8 from both sides.


y=%282%2F3%29x-10%2F3 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=%282%2F3%29x-10%2F3

Answer by Ave(106) About Me  (Show Source):
You can put this solution on YOUR website!
First find the slope
rise -8-(-6)=-2
run -7-(-4)=-3
so 2/3 is slope, then use point slope form
y-y1=slope(x-x1) pick either of the given points and plug it in to x1, y1
I'll use (-7,-8)
y-(-8)=2/3(x-(-7)) Times both sides by 3 to get rid of fraction
3y+24=2(x+7) Add a negative 24 to each side
3y=-24+2x+14 Combine like terms
3y=2x-10 Divide by 3
y=2/3x-10/3 usually written in this way (slope intercept)
standard form would be -2x+3y=-10