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How do you graph the inequality #3x+4y<=12#?

Answer 1

Graph the line of #(3x+4y=12)# using two arbitrary solutions;
then shade in the side of the line containing the point #(0,0)#

#3x+4y<=12# includes all points on the line #3x+4y=12#

The x and y intercepts provide a convenient pair of points on this line (although any other pairs would work). #color(white)("XXX")x=0 rarr y=4# #color(white)("XXX")y=0 rarr x=3# so the pairs #(0,4)# and #(3,0)# are on this line. Plot these point and draw a line through them.

Since the inequality is true for #(x,y)=(0,0)# the point #(0,0)# must be on the selected side of the line just drawn. graph{3x+4y <= 12 [-10, 10, -5, 5]}

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Answer 2

Savannah Anderson

To graph the inequality 3x + 4y ≤ 12:

First, graph the line 3x + 4y = 12.
To graph the line, find two points that satisfy the equation. One way to do this is to set x = 0 and solve for y, then set y = 0 and solve for x.
Plot these two points and draw a straight line passing through them.
Since the inequality is ≤, the region below or on the line is shaded. This represents the solutions to the inequality.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you graph the inequality #3x+4y&lt;=12#?

How do you graph the inequality #3x+4y<=12#?