Through Which Points Does the Graph of x = y - 4 + 2x Pass?

To determine through which point the function passes, we begin by simplifying the given equation.

Given: $x = y - 4 + 2x$

Rearranging the terms to solve for $y$:

$x = y - 4 + 2x$

Subtract $x$ from both sides to isolate the terms involving $y$:

$0 = y - 4 + x$

Rearrange to solve for $y$:

$y = -x + 4$

Now, we will test each point to see which satisfies the equation $y = -x + 4$.

• For $(-1, 5)$, substitute $x = -1$:

$y = -(-1) + 4 = 1 + 4 = 5$

This point satisfies the equation.

• For $(0, 5)$, substitute $x = 0$:

$y = -(0) + 4 = 4$

This point does not satisfy the equation.

• For $(1, 5)$, substitute $x = 1$:

$y = -(1) + 4 = -1 + 4 = 3$

This point does not satisfy the equation.

• For $(2, 5)$, substitute $x = 2$:

$y = -(2) + 4 = -2 + 4 = 2$

This point does not satisfy the equation.

Therefore, the graph of the function passes through the point $(-1, 5)$.