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How do you graph the inequality # y + 2<= -2/3(x - 6).#?

Answer 1

Hazel Anglin

You can rewrite the inequality in slope-intercept form:

First work away the parentheses: #y+2<=-2/3x-2/3(-6)-># #y+2<=-2/3x+4->y<=-2/3x+2#

If you graph the line of #y=-2/3x+2#, the line itself and everything under it fits the inequality.

The #y#-intercept will be #x=0->(0,2)#, the #x#-intercept will be #y=0->(3,0)# graph{-2/3x+2 [-10, 10, -5, 5]}

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Answer 2

Savannah Anderson

To graph the inequality ( y + 2 \leq -\frac{2}{3}(x - 6) ), follow these steps:

Start by rewriting the inequality in slope-intercept form: ( y \leq -\frac{2}{3}x + 4 ).
Plot the y-intercept at (0, 4).
Use the slope of -2/3 to plot another point. Since the slope is negative, move down 2 units and to the right 3 units from the y-intercept. This gives you the point (3, 2).
Draw a dashed line through these two points. Since the inequality includes "less than or equal to," use a dashed line to indicate that the points on the line are included in the solution set.
Shade the region below the dashed line to represent all the points that 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 the inequality # y + 2&lt;= -2/3(x - 6).#?

How do you graph the inequality # y + 2<= -2/3(x - 6).#?