SOLUTION: Hello I need to solve this and I havent done math for 5 years.could you please help me what is the equation of th eline that contains the points with ( x, y ) coordinates ( -3,

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello I need to solve this and I havent done math for 5 years.could you please help me what is the equation of th eline that contains the points with ( x, y ) coordinates ( -3,       Log On


   

Question 163972: Hello I need to solve this and I havent done math for 5 years.could you please help me
what is the equation of th eline that contains the points with ( x, y ) coordinates ( -3, 7 ) and (5,-1)
thanks
tha answer is y= -x + 4 can you explain why>?
Found 2 solutions by jim_thompson5910, nerdybill:
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


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


m=%28-1-7%29%2F%285--3%29 Plug in y%5B2%5D=-1, y%5B1%5D=7, x%5B2%5D=5, and x%5B1%5D=-3


m=%28-8%29%2F%285--3%29 Subtract 7 from -1 to get -8


m=%28-8%29%2F%288%29 Subtract -3 from 5 to get 8


m=-1 Reduce


So the slope of the line that goes through the points and is m=-1


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-7=-1%28x--3%29 Plug in m=-1, x%5B1%5D=-3, and y%5B1%5D=7


y-7=-1%28x%2B3%29 Rewrite x--3 as x%2B3


y-7=-1x%2B-1%283%29 Distribute


y-7=-1x-3 Multiply


y=-1x-3%2B7 Add 7 to both sides.


y=-1x%2B4 Combine like terms.


y=-x%2B4 Simplify


So the equation that goes through the points and is y=-x%2B4


Notice how the graph of y=-x%2B4 goes through the points and . So this visually verifies our answer.
Graph of y=-x%2B4 through the points and

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
If you are given two points, you can determine the slope from:
m = (y2-y1)/(x2-x1)
Our two points:( -3, 7 ) and (5,-1)
substituting it in, we get:
m = (-1-7)/(5-(-3))
m = (-8)/(5+3)
m = (-8)/(8)
m = -1
.
Now that we know the slope (-1), we can use one of the two given points (say we use ( -3, 7 )) and plug it into the "point-slope" form of a line:
y – y1 = m(x – x1)
y – 7 = -1(x – (-3))
y – 7 = -1(x + 3)
y – 7 = -x - 3
y = -x + 4 (this is our equation of the line)