# Thread: Graph the two points to find another solution.

1. ## Graph the two points to find another solution.

An equation and two ordered pairs are given. Show that each pair is a solution. Then use the graph of the two points to determine another solution.

What I have so far:

y=x-5 (4, -1) and (1, -4)

for (4, -1):
4y=-1x-5
is the same as y=-1/4x-5

for (1,-4)
1y=-4x-5
is the same as y=1/-4x-5

I'm not entirely sure how I graph these, though. Could someone give me a hand?

2. For y=x-5, you need to show that (4, -1) and (1, -4) are solutions. This means that if you plug the x- and y-coordinates in from each point into your line, you get a true statement. So first, consider (4,-1):

Put x = 4, y = -1 into your equation - this means you have to REPLACE x with 4 and REPLACE y with -1. In your original post, you just put the 4 and -1 in front of the x and y. They take the place of x and y, i.e.:

-1 = 4 - 5.

This is obviously a true statement, as 4 - 5 does equal -1. Because you get a true statement, you know the point is a solution.

Repeat this process for (1, -4).

Now, carefully plot the two points, using graph paper, and connect the points with a straight line. EVERY point your straight line passes through is another solution. On your graph, look for a point that has integer x- and y-coordinates that your line passes through (in other words, where your line crosses an intersection on the graph paper). Use that point for another solution.

Sorry I can't draw it, but if you plot the points and connect them, I think it'll be clearer.

Hope this helps!