SOLUTION: write an equation of the line that passes through (4,3) and (2,-2)

Algebra ->  Linear-equations -> SOLUTION: write an equation of the line that passes through (4,3) and (2,-2)      Log On


   

Question 118099: write an equation of the line that passes through (4,3) and (2,-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 (4,3) and (2,-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 (4,3) and is the second point (2,-2))

m=%28-2-3%29%2F%282-4%29 Plug in y%5B2%5D=-2,y%5B1%5D=3,x%5B2%5D=2,x%5B1%5D=4 (these are the coordinates of given points)

m=+-5%2F-2 Subtract the terms in the numerator -2-3 to get -5. Subtract the terms in the denominator 2-4 to get -2


m=5%2F2 Reduce

So the slope is
m=5%2F2

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


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-3=%285%2F2%29%28x-4%29 Plug in m=5%2F2, x%5B1%5D=4, and y%5B1%5D=3 (these values are given)


y-3=%285%2F2%29x%2B%285%2F2%29%28-4%29 Distribute 5%2F2

y-3=%285%2F2%29x-10 Multiply 5%2F2 and -4 to get -20%2F2. Now reduce -20%2F2 to get -10

y=%285%2F2%29x-10%2B3 Add 3 to both sides to isolate y

y=%285%2F2%29x-7 Combine like terms -10 and 3 to get -7
------------------------------------------------------------------------------------------------------------
Answer:


So the equation of the line which goes through the points (4,3) and (2,-2) is:y=%285%2F2%29x-7

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=5%2F2 and the y-intercept is b=-7

Notice if we graph the equation y=%285%2F2%29x-7 and plot the points (4,3) and (2,-2), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=%285%2F2%29x-7 through the points (4,3) and (2,-2)

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