-5x - 4y ≥ 20
Add 5x to both sides:
-4y ≥ 5x + 20
Divide both sides by -4. When multiply or divide an inequality by a negative number, you have to flip the inequality sign, in this case from ≥ to ≤
y ≤ -(5/4)x - 5
You have 0 and -5 for the x. To find the y-values, simply plug the x-values into the inequality and solve for y. I'll do x=0 for you:
y ≤ -(5/4)x - 5
y ≤ -(5/4)*(0) - 5 [Plugged 0 in in place of x]
y ≤ -5
So the point is (0,-5)
Can you figure out the y when x=-5? Hint: replace the x in the inequality with -5 and compute the y-value.
Once you have the second point, you can plot the two points on the graph and draw the line. But you still need to figure out which side of line satisfies the inequality. To do that, pick a point on one side of the line and plug the x and y values into your inequality (the points (0,0) or (1,1) are good points to try). If the inequality is true when you do that, then the side of the line containing the point is the solution; if not, it's the other side of the line. Since the inequality includes the "equal to" (≤), the line itself is also part of the solution.
