1. **Problem Statement:** Determine the slope and intercepts of the linear equation $3x + 2y = 12$ using substitution. 2. **Formula and Rules:** - The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. - The x-intercept is found by setting $y=0$ and solving for $x$. - The y-intercept is found by setting $x=0$ and solving for $y$. 3. **Find the y-intercept:** Set $x=0$ in the equation: $$3(0) + 2y = 12 \implies 2y = 12 \implies y = \frac{12}{2} = 6$$ So, the y-intercept is $(0,6)$. 4. **Find the x-intercept:** Set $y=0$ in the equation: $$3x + 2(0) = 12 \implies 3x = 12 \implies x = \frac{12}{3} = 4$$ So, the x-intercept is $(4,0)$. 5. **Rewrite in slope-intercept form:** $$3x + 2y = 12 \implies 2y = 12 - 3x \implies y = \frac{12}{2} - \frac{3}{2}x = 6 - \frac{3}{2}x$$ 6. **Identify the slope:** The slope $m = -\frac{3}{2}$. **Final answer:** - Slope: $-\frac{3}{2}$ - x-intercept: $(4,0)$ - y-intercept: $(0,6)$