Question

How do you graph the inequality $4x-4y\ge 28$ ?

Answer 1

Hint: To start with, we are trying to graph the inequality $4x-4y\ge 28$. So, we will begin with dividing both sides to get an easier form of the equation. Now, to graph the equation we can change the inequality with an equal sign. Next we will compare the equation with the slope intercept form of a straight line and thus we will find the slope and y intercept. Putting these in a graph paper will give us our solution.

Complete step by step answer:
According to the question, we are to graph the given inequality $4x-4y\ge 28$.
Now, if we divide both sides with 4, we are getting $x-y\ge 7$.
Again, whenever we try to draw any graph, we replace the inequality sign with the equal sign and then try to get on with it.
So, following that, we have, $x-y=7$
If we put x on the right side of the equation, we get, $-y=7-x$.
Multiplying both sides with -1, we will get, $y=x-7$.
Comparing this with the slope intercept form of a line, $y=mx+c$ where m is the slope and c is the intercept, we have, m = 1 and c = -7.
So, we get the straight line with the slope as 1 and a y-intercept of -7.
Hence, the solution set for our inequality is all the points greater than or equal to this line.
Now, we will try to draw the inequality with the given values.
It will look like,
 

Hence, we have the solution in the form of a graph.

Note:
While graphing an equality we are to keep some things in mind. We shade below (not above) if y is less than (or equal to) the other side of the inequality. We draw a solid line (not dashed) because we're dealing with an "or equal to" inequality. The solid line indicates that points on the line are solutions to the inequality.