Question 411546
6x - y > 6 is a linear inequality.

subtract 6x from both sides of the equation to get:


-y > 6 - 6x


multiply both sides of the equation by -1 to get:


y < 6x - 6


note that multiplying both sides of an inequality by -1 reverses the inequality.


2 > 1


multiply both sides by -1 and you get -2 < -1


you graph the inequality of y < 6x-6 by graphing the equality of y = 6x-6 and then shading the area under the line created.


the graph of y = 6x - 6 is shown below:


{{{graph(600,600,-5,5,-20,20,6x - 6,12,6)}}}


the area under that line is the area that you want.


any point in that area will satisfy the equation of y < 6x - 6


take x = 3,


this makes y = 12


any value of y < 12 will be under the line at x = 3 which puts it in the shaded area.


I showed the line y = 12 to show you where the dividing line would be when x = 3.


when x = 3, any value of y equal to or greater than 12 will not satisfy the equation of y < 6x - 6.


when x = 2, any value of y less than 6 would satisfy the equation.


I showed the line y = 6 to how you where the dividing line would be when x = 2.