SOLUTION: Write an equation of the line containing the points (2, -3) and (4, 5).

Algebra ->  Linear-equations -> SOLUTION: Write an equation of the line containing the points (2, -3) and (4, 5).      Log On


   

Question 625861: Write an equation of the line containing the points (2, -3) and (4, 5).
Found 2 solutions by jim_thompson5910, lenny460:
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=2 and y%5B1%5D=-3.
Also, is the second point . So this means that x%5B2%5D=4 and y%5B2%5D=5.


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


m=%285--3%29%2F%284-2%29 Plug in y%5B2%5D=5, y%5B1%5D=-3, x%5B2%5D=4, and x%5B1%5D=2


m=%288%29%2F%284-2%29 Subtract -3 from 5 to get 8


m=%288%29%2F%282%29 Subtract 2 from 4 to get 2


m=4 Reduce


So the slope of the line that goes through the points and is m=4


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


y%2B3=4%28x-2%29 Rewrite y--3 as y%2B3


y%2B3=4x%2B4%28-2%29 Distribute


y%2B3=4x-8 Multiply


y=4x-8-3 Subtract 3 from both sides.


y=4x-11 Combine like terms.


So the equation that goes through the points and is y=4x-11


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Answer by lenny460(1073) About Me  (Show Source):
You can put this solution on YOUR website!
Plot the straight line graph with the following points:
(2,-3)
(4,5)
From the above straight line graph:
the y-intercept is -11

Now let's find the Slope (m)
(y2 - y2)/(x2 - x1)
= (-3 - 5)/(2 - 4)
= -3 - 5 = -8
= 2 - 4 = -2
Therefore:
-8/-2 = 8/2 = 4
The Slope (m) = 4

The other method:
(5 - (-3)/(4 -2)
5 - (-3) = 5 + 3 = 8
4 - 2 = 2
8/2 = 4
The Slope (m) = 4


We now use the formula:
y = mx + b
m = slope = 4
b = y-intercept = -11
Therefore:
y = 4x - 11

The Answer:

y = 4x - 11


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