Answer:
Step 1:
To find ordered pair solutions, you could create an x and y graph and fill out the x side. Then, plug in an x number to get your y number and graph the ordered pairs to see if they give you a straight line. I'm going to use these numbers: -1, 0, 1, and 2.
[tex]...x...|...y...[/tex]
[tex]\left[\begin{array}{ccc}-1&?\\0&?\\1&?\\2&?\end{array}\right][/tex]
Now, let's plug in -1 into the equation first to see what we get for y.
[tex]y=8(-1)+3\\y=-8+3\\y=-5\\(-1,-5)[/tex]
-5 is our y if x was -1.
We do the same for the other three numbers.
[tex]y=8(0)+3\\y=0+3\\y=3\\(0,3)[/tex]
[tex]y=8(1)+3\\y=8+3\\y=11\\(1,11)[/tex]
[tex]y=8(2)+3\\y=16+3\\y=19\\(2,19)[/tex]
Step 2:
With all that done, we can now fill out our table and graph the points.
[tex]....x...|...y....[/tex]
[tex]\left[\begin{array}{ccc}-1&-5\\0&3\\1&11\\2&19\end{array}\right][/tex]
If you graph these points on graph paper / a graphing website, you will see that these points go in a straight line. If you are given an ordered pair already (for example: (3,5)), then all you have to do is plug in the x into the equation (3) and see if the outcome is true (5).
[tex]5=8(3)+3\\5=24+3\\5\neq 27[/tex]
Since they don't equal each other, then (3,5) is false.
Here is the graph for the table above. I hope I helped you!
