Questions: Lesson 23 Linear Equations in Two x 4-2 y=8-2 x x-intercept: ( ? ) Absent y-intercept: Absent

Solution Steps

To find the $x$-intercept and $y$-intercept of the linear equation $4 - 2y = 8 - 2x$, we need to follow these steps:

1. Find the $x$-intercept: Set $y = 0$ in the equation and solve for $x$.
2. Find the $y$-intercept: Set $x = 0$ in the equation and solve for $y$.

To find the $x$-intercept, we set $y = 0$ in the equation $4 - 2y = 8 - 2x$: $$4 - 2(0) = 8 - 2x \implies 4 = 8 - 2x$$ Rearranging gives: $$2x = 8 - 4 \implies 2x = 4 \implies x = 2$$ Thus, the $x$-intercept is $(2, 0)$.

To find the $y$-intercept, we set $x = 0$ in the equation: $$4 - 2y = 8 - 2(0) \implies 4 - 2y = 8$$ Rearranging gives: $$-2y = 8 - 4 \implies -2y = 4 \implies y = -2$$ Thus, the $y$-intercept is $(0, -2)$.

Final Answer