How do you graph #9y<=12x#?

1 Answer
Mar 31, 2015

To graph an inequality, try to manipulate it into the form #y \le f(x)# (or #y \ge f(x)#). Once this is done, the points which solve the inequality will be those under (or above) the graph of the function: in fact, #y=f(x)# are exactly the points of the graph. This means that #y \le f(x)# represents all the point below the graph, and vice versa #y \ge f(x)# represents all the point above the graph.

In this case, you only need to divide by 9 both sides to get
#y \le 12/9 x# which is equivalent to #y \le 4/3 x#. So, you only need to draw the #y=4/3 x# line, and take all the part of the plan below the line.

Drawing such a line is quite easy, since it crosses the origin (you can see that #(0,0)# fits in the equation, as #0=4/3*0#), and a second point, chosen as you want. For example, if #x=3# you get #y=4#. So, the line passes through the two points #(0,0# and #(3,4)#, and any line is completely determined by two of its point.

Take a look at the graph: graph{9y\le 12x [-10, 10, -5, 5]}