SOLUTION: Find the equation of the line passing through the points (-1, 4) and (5, 2).

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the line passing through the points (-1, 4) and (5, 2).      Log On


   

Question 102260: Find the equation of the line passing through the points (-1, 4) and (5, 2).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First lets find the slope through the points (-1,4) and (5,2)

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

m=%282-4%29%2F%285--1%29 Plug in y%5B2%5D=2,y%5B1%5D=4,x%5B2%5D=5,x%5B1%5D=-1 (these are the coordinates of given points)

m=+-2%2F6 Subtract the terms in the numerator 2-4 to get -2. Subtract the terms in the denominator 5--1 to get 6


m=-1%2F3 Reduce

So the slope is
m=-1%2F3

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


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 is one of the given points

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

y-4=%28-1%2F3%29%28x--1%29 Plug in m=-1%2F3, x%5B1%5D=-1, and y%5B1%5D=4 (these values are given)


y-4=%28-1%2F3%29%28x%2B1%29 Rewrite x--1 as x%2B1


y-4=%28-1%2F3%29x%2B%28-1%2F3%29%281%29 Distribute -1%2F3

y-4=%28-1%2F3%29x-1%2F3 Multiply -1%2F3 and 1 to get -1%2F3

y=%28-1%2F3%29x-1%2F3%2B4 Add 4 to both sides to isolate y

y=%28-1%2F3%29x%2B11%2F3 Combine like terms -1%2F3 and 4 to get 11%2F3 (note: if you need help with combining fractions, check out this solver)


------------------------------------------------------------------------------------------------------------
Answer:


So the equation of the line which goes through the points (-1,4) and (5,2) is:y=%28-1%2F3%29x%2B11%2F3

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1%2F3 and the y-intercept is b=11%2F3

Notice if we graph the equation y=%28-1%2F3%29x%2B11%2F3 and plot the points (-1,4) and (5,2), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=%28-1%2F3%29x%2B11%2F3 through the points (-1,4) and (5,2)

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