How do you graph the inequality y>=3/2x-3?

1 Answer
Jul 24, 2018

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Please read the explanation.

Explanation:

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We have the inequality:

color(red)(y>=(3/2)x-3

If we can find both the x-intercept and the y-intercept, we can graph.

color(green)(Step.1

To find the x-intercept, set color(blue)(y=0

Replace color(red)(>= sign to color(red)(= for this step.

y=(3/2)x-3

0=(3/2)x-3

Add color(red)(3 to both sides of the equality

rArr 0+3=(3/2)x-3+3

rArr 3=(3/2)x-cancel 3+cancel 3

rArr 3=(3/2)x

Divide both sides by color(red)(3/2

rArr x = 3*(2/3)

rArr x = cancel 3*(2/cancel 3)

color(blue)( :. x= 2

Hence, x-intercept: color(blue)((2,0) ... Res.1

color(green)(Step.2

To find the y-intercept, set color(blue)(x=0

Replace color(red)(>= sign to color(red)(= for this step.

y=(3/2)x-3

y=(3/2)(0)-3

color(blue)( :. y= -3

Hence, y-intercept: color(blue)((0,-3) ... Res.2

Use both the intermediate results, Res.1 and Res.2, and plot the points on a graph.

Join the two points color(blue)(("x-intercept" and "y-intercept)" with a Solid Line, as our inequality uses a = sign as well.

That would mean the value is a part of the solution.

color(green)(Step.3

Shading the Solution Region can be done as follows:

Use a Test Value to determine which part of the graph to shade.

Consider the point color(red)((0,0)

Substitute these values of color(blue)(x and y and test the inequality.

We have the inequality:

color(red)(y>=(3/2)x-3

rArr 0>= (3/2)*(0)-3

0>=-3

This result is color(red)("TRUE"

So, the solution region is above the line of the graph.

And hence, our inequality graph will be:

enter image source here

Solid line used indicates that the solution contains the values on the line.

Hope it helps.