SOLUTION: 1)Write the equation of the line through (1,2) and (-3,6) in the y=mx+b format. Please show all work. Thank You

Algebra ->  Graphs -> SOLUTION: 1)Write the equation of the line through (1,2) and (-3,6) in the y=mx+b format. Please show all work. Thank You       Log On


   

Question 118912: 1)Write the equation of the line through (1,2) and (-3,6) in the y=mx+b format. Please show all work.
Thank You
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 (1,2) and (-3,6)

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 (1,2) and is the second point (-3,6))

m=%286-2%29%2F%28-3-1%29 Plug in y%5B2%5D=6,y%5B1%5D=2,x%5B2%5D=-3,x%5B1%5D=1 (these are the coordinates of given points)

m=+4%2F-4 Subtract the terms in the numerator 6-2 to get 4. Subtract the terms in the denominator -3-1 to get -4


m=-1 Reduce

So the slope is
m=-1

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


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


y-2=-x%2B%28-1%29%28-1%29 Distribute -1

y-2=-x%2B1 Multiply -1 and -1 to get 1

y=-x%2B1%2B2 Add 2 to both sides to isolate y

y=-x%2B3 Combine like terms 1 and 2 to get 3
------------------------------------------------------------------------------------------------------------
Answer:


So the equation of the line which goes through the points (1,2) and (-3,6) is:y=-x%2B3

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1 and the y-intercept is b=3

Notice if we graph the equation y=-x%2B3 and plot the points (1,2) and (-3,6), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=-x%2B3 through the points (1,2) and (-3,6)

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