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

The graph of the given inequality can be drawn by finding the x-intercept and y-intercept of the line (y = 5x - 20).

Given :

Inequality  --  5x - y > 20

The following steps can be used to sketch the graph of the given inequality:

Step 1 - Write the given inequality.

5x - y > 20

Step 2 - Rewrite the above inequality.

y < 5x -20

Step 3 - Draw the graph of (y = x).

Step 4 - Now, find the y-intercept by comparing the equation (y = 5x - 20) with the slope-intercept form.

c = -20

Step 5 - Now, determine the x-intercept by substitute the value of (y = 0) in the equation (y = 5x - 20) that is:

0 = 5x - 20

x = 4

Step 6 - Now, draw the line that passes through the points (0,20) and (4,0).

Step 7 - Shade the graph of the left side of the line (y = 5x - 20). The resulting graph is the graph of (y < 5x - 20).

For more information, refer to the link given below:

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Step-by-step explanation:

Solve the inequality 5x − 4y > 20 for y, as follows:  Subtract 5x from both sides, obtaining:

-4y > 20 - 5x;

Then divide all terms by -4:

y    < -5 +(5/4)x, where the direction of the inequality sign has been reversed because of division by a negative quantity.

Temporarily replace the < symbol with =     obtaining    y = -5 +(5/4)x.  Now choose at least three x values and find the corresponding y values.  For example:

 x      y = -5 +(5/4)x  

 0          -5

 4            0

 -8         -15

Now plot these three points (0, -5), (4, 0) and (-8, -15).  Draw a dashed line through them.  Because of the < symbol in y    < -5 +(5/4)x, shade the area underneath the dashed line.

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