The equation 2x + 3y = 12 in slope-intercept form is y = mx + b. Which equation correctly represents it?

The equation 2x + 3y = 12 in slope-intercept form is y = mx + b. Which equation correctly represents it?

• A. y = (-2/3)x + 4
• B. y = (2/3)x + 4
• C. y = (-3/2)x + 4
• D. y = (-2/3)x - 4

Answer: (A)

To rewrite in slope-intercept form, solve for y. Start with 2x + 3y = 12. Subtract 2x from both sides to get 3y = -2x + 12. Divide every term by 3: y = (-2/3)x + 4. The slope is -2/3 and the y-intercept is 4, which matches the required y = mx + b form. The negative sign on the x-term shows the slope is negative, and the constant term 4 comes from 12 divided by 3. The other possibilities would have the wrong slope sign or the wrong intercept.

To rewrite in slope-intercept form, solve for y. Start with 2x + 3y = 12. Subtract 2x from both sides to get 3y = -2x + 12. Divide every term by 3: y = (-2/3)x + 4. The slope is -2/3 and the y-intercept is 4, which matches the required y = mx + b form. The negative sign on the x-term shows the slope is negative, and the constant term 4 comes from 12 divided by 3. The other possibilities would have the wrong slope sign or the wrong intercept.