when dealing with linear equations

Question

I have a equations such as 3x-3y=9 I am curious on how to set up and solve this equation and how the graphing lines should look like

Answer 1

The equation:

     3x - 3y = 9

is exactly the same line as:

     x - y = 3                        [divide each term by 3]

 

Two points determine a line.  To graph this line let:

     x=0 to find the y-intercept (the point where the line crosses the x-axis)  at (0,-3)

     y=0 to find the x-intercept (the point where the line crosses the y-axis)  at (3,0)

Note: the equation may make it easier to select a different point(s).

This form of the equation of a line is called Standard Form (Ax+By=C)

 

With slope-intercept form (y=mx+b, where m=slope [often called "rise over run" because it measures increase in y-values divided by increase in x-values] and b is the y-intercept), you may start at any point and use the slope to find another point (by moving the appropriate x-value and y-value -- also note: negative means left or down).

 

So, if you have the point (3,0) and know that the slope is 1 [y=1x-3], then (3+1, 0+1) or (4,1) is also on the line.

 

Also, to "solve" means to find the point(s) that satisfy all the equations in a system (that is, the point or area where all equations or inequalities are true).