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Graph the solution set of this inequality:

5x − 4y > 20.

Graph the solution set of this inequality: 5x − 4y > 20.-example-1

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Answer:

See below

Explanation:

To graph the solution set of the inequality
\sf 5x - 4y > 20, we'll first rewrite it in slope-intercept form (
\sf y = mx + b), where
\sf m is the slope and
\sf b is the y-intercept.


\sf 5x - 4y > 20

Subtract
\sf 5x from both sides:


\sf 5x - 4y -5x> -5x20

[tex]\sf -4y > -5x + 20[/tex]

Divide both sides by
\sf -4 (note that when dividing by a negative number, the inequality sign flips):


\sf y < (5)/(4)x - 5

Now, we can graph the corresponding line
\sf y = (5)/(4)x - 5 and shade the region below it because we have
\sf y < (5)/(4)x - 5.

Here's how we can graph it:

1. Plot the y-intercept at
\sf y = -5. This gives us the point (0, -5).

2. Use the slope
\sf (5)/(4) to find another point. For example, move up 5 units and to the right 4 units from the y-intercept, giving we the point (4, 0).

3. Draw a dashed line through these two points.

Now, since we have
\sf y < (5)/(4)x - 5, shade the region below the line.

The shaded region represents the solution set of the inequality
\sf 5x - 4y > 20.

Graph the solution set of this inequality: 5x − 4y > 20.-example-1
User BendEg
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