What is the slope of the line represented by the equation 2x + 3y= -12. (A)- 3/2. (B)-2/3. (C) 2/3. (D) 3/2

-2/3

Explanation:
The equation in the question is written in the standard form of a linear equation.

Standard form: Ax+By=C

A, B and C don’t have any direct interpretation on a graph, so we can’t identify the slope or really any information about the line when the equation is in standard form.

To identify the slope from an equation, we have to change it to slope-intercept form.

Slope-intercept form: y=mx+b

Here’s what the variables mean:

Y= the y-coordinate
M=the slope
X=the x-coordinate
B= the y-intercept (the point on the line that intercepts the y-axis)

1) Rearrange the equation
2x+3y=-12
Subtract both sides by 2x to isolate 3y
-2x+2x+3y=-2x-12
3y=-2x-12
Divide both sides by 3 to isolate y
3y/3=-2/3x-12/3
y=-2/3x-4

2) Identify the m variable
The value in place of the m variable in y=mx+b represents the slope. From the equation above, we can see clearly that -2/3x is in place of the m variable. Here’s a comparison:

y=mx+b
y=-2/3x-4

Therefore, the slope of the line represented by the equation 2x+3y=-12 is -2/3.

I hope this helps! Please comment if you have any questions.

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