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How do you graph #4y<=-6# on the coordinate plane?

Answer 1

Hazel Anglin

See a solution process below:

Divide each side of the inequality by #color(red)(4)# to solve for #y# while keeping the inequality balanced:

#(4y)/color(red)(4) <= -6/color(red)(4)#

#(color(red)(cancel(color(black)(4)))y)/cancel(color(red)(4)) <= -6/4#

#y <= -3/2#

To graph this we will draw a horizontal line at #-3/2# on the vertical axis.

The line will be a solid line because the inequality operator contains an "or equal to" clause.

We will shade to the below the line because the inequality operator also contains a "less than" clause:

graph{y<=-3/2 [-10, 10, -5, 5]}

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Answer 2

Avery Alexander

To graph the inequality (4y \leq -6) on the coordinate plane, first, plot the line (y = -\frac{6}{4}), which simplifies to (y = -\frac{3}{2}). Since the inequality includes points where (y) is less than or equal to (-\frac{3}{2}), the line should be drawn as a solid line. Then, shade the region below the line, as all points with (y) values less than or equal to (-\frac{3}{2}) satisfy 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 #4y&lt;=-6# on the coordinate plane?

How do you graph #4y<=-6# on the coordinate plane?