Final answer:
The slope of the equation 3x - 2y > 12 is 3/2, and the y-intercept is -6 once it's rearranged into slope-intercept form as y < 3/2x - 6.
Step-by-step explanation:
To find the slope and y-intercept of the inequality 3x - 2y > 12, we should first express the inequality in slope-intercept form, which is y = mx + b; where m represents the slope, and b represents the y-intercept.
First, isolate the y variable:
- Subtract 3x from both sides: -2y > -3x + 12.
- Divide both sides by -2, remembering to reverse the inequality symbol because we're dividing by a negative number: y < 3/2x - 6.
The resulting equation, y < 3/2x - 6, tells us the slope of the boundary line is 3/2 and the y-intercept is -6. Please note that since this is an inequality, we are considering values of y that are less than this line, not the line itself.