1. Find the intercepts for the equation $2x + y = 8$. - To find the x-intercept, set $y = 0$: $$2x + 0 = 8 \implies 2x = 8 \implies x = 4$$ - To find the y-intercept, set $x = 0$: $$2(0) + y = 8 \implies y = 8$$ 2. Find the intercepts for the equation $3x - 2y = 6$. - X-intercept ($y=0$): $$3x - 2(0) = 6 \implies 3x = 6 \implies x = 2$$ - Y-intercept ($x=0$): $$3(0) - 2y = 6 \implies -2y = 6 \implies y = -3$$ 3. Find the intercepts for the equation $x + 4y = 12$. - X-intercept ($y=0$): $$x + 4(0) = 12 \implies x = 12$$ - Y-intercept ($x=0$): $$0 + 4y = 12 \implies 4y = 12 \implies y = 3$$ 4. Find the intercepts for the equation $5x - y = 10$. - X-intercept ($y=0$): $$5x - 0 = 10 \implies 5x = 10 \implies x = 2$$ - Y-intercept ($x=0$): $$5(0) - y = 10 \implies -y = 10 \implies y = -10$$ 5. Find the intercepts for the equation $4x + 2y = 16$. - X-intercept ($y=0$): $$4x + 2(0) = 16 \implies 4x = 16 \implies x = 4$$ - Y-intercept ($x=0$): $$4(0) + 2y = 16 \implies 2y = 16 \implies y = 8$$ Summary: - 1: x-intercept = 4, y-intercept = 8 - 2: x-intercept = 2, y-intercept = -3 - 3: x-intercept = 12, y-intercept = 3 - 4: x-intercept = 2, y-intercept = -10 - 5: x-intercept = 4, y-intercept = 8