SOLUTION: 1. Write the equation of the line through (1,2) and (-3,6) in the y=mx+b format. 2.. Solve x + y - z = 0 2x - y + z = 6 -x + y + z = 8 Show your answer

Question 83597: 1. Write the equation of the line through (1,2) and (-3,6) in the y=mx+b format.
2.. Solve
x + y - z = 0
2x - y + z = 6
-x + y + z = 8
Show your answers as (x,y,z)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
1.

Solved by pluggable solver: Finding the Equation of a Line

First lets find the slope through the points (,) and (,)

Start with the slope formula (note: (,) is the first point (,) and (,) is the second point (,))

Plug in ,,, (these are the coordinates of given points)

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get

Reduce

So the slope is

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

------Point-Slope Formula------
where is the slope, and (,) is one of the given points

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

Plug in , , and (these values are given)

Distribute

Multiply and to get . Now reduce to get

Add to both sides to isolate y

Combine like terms and to get

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Answer:

So the equation of the line which goes through the points (,) and (,) is:

The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is

Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver )

Graph of through the points (,) and (,)

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

2.
Start with the given system and label the equations
Equation 1
Equation 2
Equation 3
Add equations 1 and 2
Divide both sides by 3

Now lets use this info to find another variable

Plug in x=2 into equation 2 to get Equation 4
Multiply
Plug in x=2 into equation 3 to get Equation 5
Multiply equation 3 by -1

So now we have the equations
Equation 4
Equation 5
Add equations 4 and 5
Subtract 6 from both sides
Divide both sides by -2

Now lets use this to find z

Plug in x=2 and y=4 into Equation 1 (at this point any equation will do)
Add
Subtract
Divide

So our solution is
(2,4,6)
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