SOLUTION: Hello I really need some help with this math problem it deal with Coordinate Geometry: Linear Equations in Two Variables. What is the equation of the line that contains the poin

Question 117320: Hello I really need some help with this math problem it deal with Coordinate Geometry: Linear Equations in Two Variables.
What is the equation of the line that contains the points with (x,y) coordinates (-3,7) and (5,-1) ?
I don't have clue how to set this type of problem up, please help.
thanks

Found 3 solutions by jim_thompson5910, checkley71, Fombitz:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
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

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

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)

Rewrite as

Distribute

Multiply and to get

Add to both sides to isolate y

Combine like terms and to get
------------------------------------------------------------------------------------------------------------
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.
Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!
FIRST YOU NEED TO FIND THE SLOPE:
SLOPE=(Y2-Y1)/(X2-X1)
SLOPE=(-1-7)/(5+3)
SLOPE=-8/8
SLOPE=-1
USING THE SLOPE (m) AND A SET OF (X,Y) VALUES IN THE LINE EQUATION Y=mX+b SOLVE FOR (b), THE Y INTERCEPT.
7=-1*-3+b
7=3+b
b=7-3
b=4
THUS THE EQUATION IS:
Y=-X+4
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
You need to use the point-slope method of a line.
First calculate the slope, m.
It's the change in y divided by the change in x.
Your points are given as (x,y) pairs.
Your first point is (-3,7).
Your second point is (5,-1).

That means that the change in y is equal to the change in x (all except the negative).
The slope is negative which means as x gets larger, y gets smaller.
You can generate points on your line using this.
Add 1 to x.
Subtract 1 from y.
(-3,7)
(-2,6)
(-1,5)
(0,4)
(1,3)
(2,2)
(3,1)
(4,0)
(5,-1)

Next, use the point slope form of the line.

where m is the slope you just calculated.
(,) are either of the two points you already know.

Use the first point (-3,7)

We would have gotten the same answer if we used the second point.

Use the second point (5,-1)

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