Answer:
This problem, in essence, is a 2 step problem. In order to find the equation of a line passing through a given point we would need to find the slope, or the rate of change. The rate of change is simply put, the change in y over the change in x. I've heard it said as "rise over run" as well.
In order to find the slope we would need to use the slope formula
the "2" and "1" in the formula is just a way to differentiate with the ordered pairs being used. Whichever y value you were to use for y2, x2 must correspond to that y value, DO NOT MIX AND MATCH or you will yield an untrue statement.
So, we have the Ordered Pairs of (5,-1) and (-5,11). I am going to let (5,-1) be my (x2,y2). So I will set up the slope formula as follows:
(-1)-(11)
(5)-(-5)
Evaluate
-12
10
Simplify
-6
5
So, we now know that the slope of a line that passes through these 2 points is -6/5. This is where it can get a little tricky. We like to express the equation of a line in what we call "Slope-Intercept form" written in the form "y=mx+b" where "m" is the slope (which we just found out) and "b" the "y-intercept", or where the line crosses the y-axis. There are 2 ways to do this;
1) Use the point slope formula, which is: y-y1=m(x-x1) where x1 and y1 are the respective values of a point that you choose. or
2) use the slope intercept form y=mx+b and solve for b. I prefer 2 so I am going to solve that way.
First, choose a point that you wish to use. We were given 2 points, so I will use one of those (5,-1).
Next, we will plug values into the slope intercept form;
y=mx+b~~we just solved for the slope previously and got a value of (-6/5) and we will use the point (5,-1)
(-1)= (-6/5)(5)+b~~evaluate and solve
-1=-6+b
+6 +6
5 = b
If you are unsure you can always check yourself by using the other point to see if you get the same answer. So, we will do just that:
y=mx+b
(11)=(-6/5)(-5)+b
11 = 30/5 + b
11 = 6 + b
-6 -6
5 = b.
Both attempts yielded a true statement, therefore, we can conclude that the equation of a line that passes through the above given points is y=(-6/5)x+5
You can also check by graphing and verifying in the table if the 2 points are on the line.
