Question

In the xy-plane, what is the slope of the line whose equation is \( 3x - 2y = 8 \)?

• A. -4
• B. \( -\frac{8}{3} \)
• C. \( \frac{2}{3} \)
• D. \( \frac{3}{2} \)
• E. 4

Hint:

To find the slope from an equation, isolate \( y \) and identify the coefficient of \( x \).

Answer 1

The Correct Option is C

To find the slope of the line, rewrite the equation \( 3x - 2y = 8 \) in slope-intercept form, \( y = mx + b \), where \( m \) is the slope: \[ 3x - 2y = 8 \implies -2y = -3x + 8 \implies y = \frac{3}{2}x - 4 \] Thus, the slope \( m = \frac{3}{2} \).
Final Answer: \[ \boxed{\frac{3}{2}} \]