1. **Problem Statement:** Find the x-intercept and y-intercept for each linear equation without graphing. The x-intercept is where $y=0$, and the y-intercept is where $x=0$. 2. **Formula and Rules:** - To find the x-intercept, set $y=0$ and solve for $x$. - To find the y-intercept, set $x=0$ and solve for $y$. 3. **(a) Equation: $y = -3x + 6$** - Find x-intercept: Set $y=0$: $$0 = -3x + 6$$ $$3x = 6$$ $$x = 2$$ So, x-intercept is $(2, 0)$. - Find y-intercept: Set $x=0$: $$y = -3(0) + 6 = 6$$ So, y-intercept is $(0, 6)$. 4. **(b) Equation: $4y = 2x - 1$** - Find x-intercept: Set $y=0$: $$4(0) = 2x - 1$$ $$0 = 2x - 1$$ $$2x = 1$$ $$x = \frac{1}{2}$$ So, x-intercept is $\left(\frac{1}{2}, 0\right)$. - Find y-intercept: Set $x=0$: $$4y = 2(0) - 1 = -1$$ $$y = -\frac{1}{4}$$ So, y-intercept is $(0, -\frac{1}{4})$. 5. **(c) Equation: $3x - 2y = 6$** - Find x-intercept: Set $y=0$: $$3x - 2(0) = 6$$ $$3x = 6$$ $$x = 2$$ So, x-intercept is $(2, 0)$. - Find y-intercept: Set $x=0$: $$3(0) - 2y = 6$$ $$-2y = 6$$ $$y = -3$$ So, y-intercept is $(0, -3)$. **Final answers:** - (a) x-intercept: $(2, 0)$, y-intercept: $(0, 6)$ - (b) x-intercept: $\left(\frac{1}{2}, 0\right)$, y-intercept: $(0, -\frac{1}{4})$ - (c) x-intercept: $(2, 0)$, y-intercept: $(0, -3)$