Let's say for example you wanted to graph the linear equation [tex]y = 2x+5[/tex]
At minimum, we'll need 2 points to form this line.
To get any point of the form (x,y), we plug in a number for x to find a corresponding number for y.
For example, replace x with 0 to find that...
[tex]y = 2x+5\\\\y = 2(0)+5\\\\y = 0+5\\\\y = 5\\\\[/tex]
Therefore, x = 0 leads to y = 5. So the point (0,5) is on the line.
Then we repeat this process for other x values. Let's try x = 1
[tex]y = 2x+5\\\\y = 2(1)+5\\\\y = 2+5\\\\y = 7\\\\[/tex]
Telling us that (1,7) is also on this line. We have enough to graph this equation. Plot the two points (0,5) and (1,7). Then draw a straight line through them. Extend this line as far as you can to the left and right. The graph is shown below.
We can keep going to get other points like (2,9) and (3,11) and (4,13) and so on. A table is a way to keep track of the xy values.
[tex]\begin{array}{|c|c|}\cline{1-2}\text{x} & \text{y}\\ \cline{1-2}0 & 5\\ \cline{1-2}1 & 7\\ \cline{1-2}2 & 9\\ \cline{1-2}3 & 11\\ \cline{1-2}4 & 13\\ \cline{1-2}\end{array}[/tex]
Each time x goes up by 1, y goes up by 2. This directly ties to the slope of 2/1 = 2.
