SOLUTION: write the equation of the line passing through: (2, -3) and (6,2)

Algebra ->  Graphs -> SOLUTION: write the equation of the line passing through: (2, -3) and (6,2)      Log On


   

Question 294740: write the equation of the line passing through: (2, -3) and (6,2)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (2,-3) and (6,2)


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 (2,-3) and (x%5B2%5D,y%5B2%5D) is the second point (6,2))


m=%282--3%29%2F%286-2%29 Plug in y%5B2%5D=2,y%5B1%5D=-3,x%5B2%5D=6,x%5B1%5D=2 (these are the coordinates of given points)


m=+5%2F4 Subtract the terms in the numerator 2--3 to get 5. Subtract the terms in the denominator 6-2 to get 4



So the slope is

m=5%2F4





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


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=%285%2F4%29%28x-2%29 Plug in m=5%2F4, x%5B1%5D=2, and y%5B1%5D=-3 (these values are given)



y%2B3=%285%2F4%29%28x-2%29 Rewrite y--3 as y%2B3



y%2B3=%285%2F4%29x%2B%285%2F4%29%28-2%29 Distribute 5%2F4


y%2B3=%285%2F4%29x-5%2F2 Multiply 5%2F4 and -2 to get -10%2F4. Now reduce -10%2F4 to get -5%2F2

y=%285%2F4%29x-5%2F2-3 Subtract 3 from both sides to isolate y


y=%285%2F4%29x-11%2F2 Combine like terms -5%2F2 and -3 to get -11%2F2 (note: if you need help with combining fractions, check out this solver)



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

Answer:



So the equation of the line which goes through the points (2,-3) and (6,2) is:y=%285%2F4%29x-11%2F2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=5%2F4 and the y-intercept is b=-11%2F2


Notice if we graph the equation y=%285%2F4%29x-11%2F2 and plot the points (2,-3) and (6,2), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%285%2F4%29x-11%2F2 through the points (2,-3) and (6,2)


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