SOLUTION: Describe the process for finding the equation of a line if you are given two points on the line.

Algebra ->  Linear-equations -> SOLUTION: Describe the process for finding the equation of a line if you are given two points on the line.       Log On


   

Question 87793: Describe the process for finding the equation of a line if you are given two points on the line.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Say you had the two points (1,-3) and (2,4) and you wanted to find the equation of the line through them

Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (1,-3) and (2,4)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (1,-3) and (x%5B2%5D,y%5B2%5D) is the second point (2,4))


m=%284--3%29%2F%282-1%29 Plug in y%5B2%5D=4,y%5B1%5D=-3,x%5B2%5D=2,x%5B1%5D=1 (these are the coordinates of given points)


m=+7%2F1 Subtract the terms in the numerator 4--3 to get 7. Subtract the terms in the denominator 2-1 to get 1



So the slope is

m=7





------------------------------------------------


Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and (x%5B1%5D,y%5B1%5D) is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y--3=%287%29%28x-1%29 Plug in m=7, x%5B1%5D=1, and y%5B1%5D=-3 (these values are given)



y%2B3=%287%29%28x-1%29 Rewrite y--3 as y%2B3



y%2B3=7x%2B%287%29%28-1%29 Distribute 7


y%2B3=7x-7 Multiply 7 and -1 to get -7%2F1. Now reduce -7%2F1 to get -7

y=7x-7-3 Subtract 3 from both sides to isolate y


y=7x-10 Combine like terms -7 and -3 to get -10

------------------------------------------------------------------------------------------------------------

Answer:



So the equation of the line which goes through the points (1,-3) and (2,4) is:y=7x-10


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=7 and the y-intercept is b=-10


Notice if we graph the equation y=7x-10 and plot the points (1,-3) and (2,4), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=7x-10 through the points (1,-3) and (2,4)


Notice how the two points lie on the line. This graphically verifies our answer.