Parallel Line Equations

First you need to calculate the slope of the line containing (2,3) and (1,-2). You do this by slope (m) = delta y / delta x.

m = (3 - - 2) / (2-1) = 5/1 = 5

(if it helps, graph this).

Then, you need to calculate the y intercept (b) for the line passing through (2,3) and (1,-2). Since you have two points, you can do this calculation twice. If you get the same answer each time, you know you are right.

For the first point, y=mx+b
3=(5)(2)+b
3=10+b
-7=b

For the second point, y=mx+b
-2=(5)(1)+b
-2=5+b
-7=b

So, the line passing through (2,3) and (1,-2) has the equation:
y=5x-7

(hint: plug in the x and y values for the two points to check the work)

Now what do we know about parallel lines? The slope must be the same. So, the equation you are looking for must be in the form of:

y=5x+b where b is the y intercept.

To get the y intercept, plug in the x and y values you were given in the problem statement:

2=(5)(-3) +b
2=-15+b
17=b

so the answer is: y=5x+17

to check the work:

2=(5)(-3)+17
2=-15+17
2=2

Hope this helps.

Jim, we only need to figure out the slope of the line goes through (2,3) and (1, -2), which is 5. The equation for that line is not necessary.