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Graph 3x-2y>-14

by Jordan
(Florida)










































How do you graph 3x-2y>-14?

Probably the easiest way to understand how to graph this inequality is to prepare an x-y table, and then plot the points listed in the table.

Begin by replacing the > designation with an = sign, and then rewrite the equation in slope intercept format.

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Dec 23, 2011
Graph 3x - 2y > -14
by: Staff


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Part II


STEP 4: Plot the three points listed in the x-y table in Step 3 on Cartesian Graph Paper.



Open the following link to view a plot of these three points:

(1) If your browser is Firefox, click the following link to VIEW the solution; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:


http://www.solving-math-problems.com/images/graph-3-points-2011-12-22-1.png

Use the Backspace key to return to this page:



STEP 5: Draw a “dashed” straight line (NOT a solid straight line) through all three points and shade the area under the curve.

The “dashed” straight line means that the solution does not include the values of x and y which are on the line. The solution includes only those values of x and y up to (but not including) the values along the line.

[Use a dashed line when the inequality uses a greater than or less than symbol: y < , or y >

Use a solid line (instead of a dashed line) when the inequality uses a greater than or equal, or less than or equal symbol: y ≤ , or y ≥ ]

The area under the curve is shaded because all values of y in the solution are less than the values along the curve: y < (3/2)*x + 7 (from Step 1).


Open the following link to view the final graph and solution of the inequality. The solution to the inequality is the entire shaded area (but does not include the dashed line):

(1) If your browser is Firefox, click the following link to VIEW the solution; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:


http://www.solving-math-problems.com/images/graph-3-points-line-graph-2011-12-22-2.png

Use the Backspace key to return to this page:



Thanks for writing.


Staff
www.solving-math-problems.com


Dec 23, 2011
Graph 3x - 2y > -14
by: Staff


Part I

Question:

by Jordan
(Florida)


How do you graph 3x - 2y > -14?


Answer:

3x - 2y > -14

Plotting inequalities can be a lot of fun.

Probably the easiest way to understand how to graph this inequality is to prepare an x-y table, and then plot the points listed in the table.


You can follow the four steps below to plot the graph using this method:

STEP 1: Solve for the variable “y”.

3x - 2y > -14 is written in the standard form

Solve for “y” to rewrite the equation in the slope-intercept form

3x - 2y + 2y > -14 + 2y

3x + 0 > -14 + 2y

3x > -14 + 2y

3x + 14 > -14 + 14 + 2y

3x + 14 > 0 + 2y

3x + 14 > 2y

(3x + 14)/2 > 2y/2

(3x + 14)/2 > y*(2/2)

(3x + 14)/2 > y*(1)

(3x + 14)/2 > y

y < (3x + 14)/2

y < 3x/2 + 14/2

y < 3x/2 + 7

y < (3/2)*x + 7

“y” is LESS THAN (3/2)*x + 7

the slope intercept form of the inequality is: y < (3/2)*x + 7


STEP 2: Temporarily change the inequality into an equation by replacing the < symbol with an = symbol.

y < (3/2)*x + 7

y = (3/2)*x + 7


STEP 3: Prepare the x-y table using the equation from Step 2.

Using the slope intercept form of the equation from Step 2, choose a value for x, and then compute y for at least three points.

Although you could plot the graph with just two sets of x-y coordinates, you should compute at least three different sets of coordinates points to ensure you have not made a mistake. All three x-y coordinates must lie on the same straight line. If they do not, you have made a mistake.

You can choose any value for x.


For example, (arbitrarily) choose x = -2

If x = -2,

y = (3/2)*x + 7

y = (3/2)*(-2) + 7

y = 4

The first set of x-y coordinates = (-2, 4), since x = -2 and y = 4.



(arbitrarily) choose x = 0


If x = 0,

y = (3/2)*x + 7

y = (3/2)*(0) + 7

y = 7

The second set of x-y coordinates = (0, 7), since x = 0 and y = 7.



(arbitrarily) choose x = 2

If x = 2,

y = (3/2)*x + 7

y = (3/2)*(2) + 7

y = 10

The third set of x-y coordinates = (2, 10), since x = 2 and y = 10.


The x-y table will look like this:

(x, y)

(-2, 4)
(0, 7)
(2, 10)


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