Lines and Equations
⇒ We have built tables and plotted points for equations in the standard form:
Ax + By = C or the
slopeintercept form: y = m x + b and noted that (a , 0), or (x_{0} , 0), is the xintercept and
(0, b), or (0, y_{0}), is the yintercept.
⇒ Now let us explore another equation given the slopeintercept form: y = m x + b:
where m is the slope and b (0 , b) is the yintercept: y = mx + b.
Example.
Graph the linear equation 3x  2y = 6 or
Compare this equation to the given the slopeintercept form: y = m x + b:
⇒ Write the slope
and the yintercept b =  6 or (0, b) = (0,  6 ).
Use the fact that the slope is
to find dx = 2 and dy = 3
Now, build a table using the common differences. On the table put the point where x = 0 in the
middle of the xsequence, add dx to get the next value below, and complete the xsequence.
Look at the given table and see how it is started. Since both columns must be arithmetic sequences
use the value for dy and add it to b in the point (0, b) to complete the table and plot the points.
Build the table and plot the points: 3x  2y = 6

x 
y 

4 
9 
dx = 2 
2 
6 
dy = 3 

0 
3 

2 
0 

4 
3 
Check the a point (6, 6) not on your table by replacing x and y in the given equation.
3x  2y = 6 → 3(6)  2(6) = 6
