graph inequality on a plane

4x+5y is less than or equal to 20

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To graph the inequality 4x + 5y ≤ 20 on a plane, follow these steps:

Step 1: Write the equation in slope-intercept form (y = mx + b), where m is the coefficient of x and b is the constant term.
In this case, rearrange the inequality to:
5y ≤ -4x + 20

Step 2: Convert the inequality to an equation. To do this, remove the inequality sign and replace it with an equal sign:
5y = -4x + 20

Step 3: Solve the equation for y:
Divide both sides of the equation by 5 to isolate y:
y = (-4/5)x + 4

Step 4: Plot the y-intercept. The y-intercept is the point where the line crosses the y-axis. In the equation y = (-4/5)x + 4, the y-intercept is b, which is 4. Plot the point (0, 4) on the plane.

Step 5: Find another point on the line. To do this, choose any value for x and plug it into the equation y = (-4/5)x + 4. Let's choose x = 5:
y = (-4/5)(5) + 4
y = -4 + 4
y = 0
Therefore, another point on the line is (5, 0).

Step 6: Connect the points. Use a straight edge or ruler to draw the line through the two points plotted in steps 4 and 5.

Step 7: Determine the region that satisfies the inequality. Since the inequality is less than or equal to, we shade the area below the line. This indicates the set of points that satisfy the inequality 4x + 5y ≤ 20.

That's how you graph the inequality 4x + 5y ≤ 20 on a plane.