What are the attributes of the boundary line of this inequality? -3x − 2y < 6

The line with an inequality equation -3x - 2y < 6 when plotted on the graph, occupies a region with a dashed boundary line with the attributes, the slope m = -3/2, and the y-intercept c = -3.

What is an inequality equation of a line?

An inequality equation for a line is the equation that is true for certain values of its variables. The inequality symbols are ' <, >, ≤, ≥ '.

How do graph an inequality?

When inequality is graphed,

The region of values for which the inequality becomes true is shaded.
If the inequality has < or > symbols, then the boundary of that region is represented with the dashed line.
If the inequality has ≤ or ≥ symbols, then the boundary of that region is represented with the solid line (no breaks).

Writing the given inequality in the slope-intercept form of a line:

The inequality equation is re-arranged in the slope-intercept form to know the attributes of the line such as the slope of the line and the y-intercept of the line.

The given inequality is -3x - 2y < 6

Step 1: Rewriting the equation into the slope-intercept form:

-3x - 2y < 6

To change the sign, change the inequality symbol also.

⇒ 3x + 2y > 6

⇒ 2y > 6 - 3x

⇒ y > -3/2x - 3

Therefore, the obtained equation is in the slope-intercept form.

So, m = -3/2 and c = -3

Step 2: Graphing the inequality:

To graph the line, we need coordinates.

So, consider x = 0 inorder to get y-coordinate

On substituting,

-3(0) -2y = 6

y = -3

∴ (0, -3) is one of the coordinates of the line

Then, consider y = 0 inorder to get x-coordinate

On substituting,

-3x - 2(0) = 6

x = -2

∴ (-2, 0) is one of the coordinates of the line

These points are plotted in the graph and a line is drawn from these points.

Step 3: Observations from the graph:

Since the inequality is -3x -2y < 6 ( < ), the region above the line is shaded ( the values that satisfies the inequality).
The line is represented as a dashed line that indicates the boundary for the inequality region.
This means the line is excluded from the solution set of the given inequality.

Therefore, the attributes of the boundary line (dashed line) are slope -3/2 and y-intercept -3.

Learn more about the graph of the inequalities here:

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