What is the slope of the straight line represented by the equation 2x + 3y = 12?

Introduction / Context:
This coordinate geometry question checks whether you can convert a line from its standard form to slope intercept form. Once the line is written as y = mx + c, the slope m can be read directly. Understanding this skill is important for graphing and analysing linear equations.

Given Data / Assumptions:

• Equation of the line: 2x + 3y = 12.
• We need to find the slope of this line.
• The coordinate system is the usual Cartesian plane.

Concept / Approach:
The slope intercept form of a line is y = mx + c, where m is the slope and c is the y intercept. To find the slope from an equation given in standard form Ax + By + C = 0 or Ax + By = C, we solve for y and compare with y = mx + c to identify m.

Step-by-Step Solution:
Step 1: Start from the given equation: 2x + 3y = 12.Step 2: Isolate the term involving y: 3y = -2x + 12.Step 3: Divide every term by 3 to solve for y: y = (-2 / 3)x + 4.Step 4: Now the equation is in the form y = mx + c with m = -2 / 3 and c = 4.Step 5: Therefore, the slope of the line is -2 / 3.

Verification / Alternative check:
You can find the slope by calculating the change in y over the change in x between any two points on the line. For example, when x = 0, y = 4; when x = 3, y = 2. Then slope = (2 - 4) / (3 - 0) = -2 / 3, which matches the result.

Why Other Options Are Wrong:
2/3 and 3/2 have the wrong sign or magnitude. The option -3/2 is the reciprocal with negative sign, which is not correct here. The value 1/2 has no relation to the coefficients of x and y in the given equation.

Common Pitfalls:
Students sometimes forget to divide the constant term when isolating y or they misplace the negative sign during rearrangement. Always solve carefully for y and then read the slope from the coefficient of x.

Final Answer:
The slope of the line 2x + 3y = 12 is -2/3.