two point variables

Question

I am still having problems figuring out this. It is Graphs of Linear Inequalities in Two Variables,

I am looking for the answer for the graph.
I have 0 and -5 for the x I need to figure out the y

-5x-4y≥20

Answer 1

Shawna,

 

First re-arrange the equation so that the y is on the left by itself:

-5x - 4y >= 20

      - 4y >= + 5x + 20

        - y >= +(5/4)x + (20/4)

          y <= - (5/4)x - 5 , note when you multiple or divide both sides by a negative 1 you must flip the inequality

 

Now plot the line which is when the equality is true for any x

y = mx + b  = -(5/4)x -5 so slope is -(5/4) and y-intercept (when x=0) is -5 on the y-axis

and y = -(5/4)(-5) -5  =  25/4 -5 = 25/4 -20/4 = 5/4

So the straight line passes thru the two points (x,y) = (0, -5) and (-5, +5/4)  and note y=0 at x = -4.

 

Finally, find the y that satisfy the inequality on y < [-(5/4)x - 5] which says all y below your plotted equality line.

So for any value x, y must be either on the line (the equality condition) or below it (governed by the inequality).