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

Find the \(x\)-intercept: Set \(y = 0\) in the equation and solve for \(x\).
Find the \(y\)-intercept: Set \(x = 0\) in the equation and solve for \(y\).

Transcript text: Lesson 23 Linear Equations in Two $x$ \[ 4-2 y=8-2 x \] $x$-intercept: $(\square$ ? $\square$ $\square$ ) Obsent $y$-intercept: $\qquad$ $\square$ ) Oabsent

Solution

Solution Steps

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

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

Step 1: Find the $x$-intercept

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 $(2, 0)$.

Step 2: Find the $y$-intercept

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 $(0, -2)$.