The problem provides a table of $x$ and $y$ values that satisfy the linear relation $y = mx + c$. We are given $x$ values of 0, 2, and 4, with corresponding $y$ values of 1, 2, and 3. The task is to find the value of $x$ when $y = 5$.

1. Problem Description

The problem provides a table of $x$ and $y$ values that satisfy the linear relation $y = mx + c$. We are given $x$ values of 0, 2, and 4, with corresponding $y$ values of 1, 2, and

3. The task is to find the value of $x$ when $y = 5$.

2. Solution Steps

First, we need to determine the values of $m$ and $c$ in the equation $y = mx + c$.

Using the point (0, 1), we can substitute $x = 0$ and $y = 1$ into the equation:

$1 = m(0) + c$

$1 = 0 + c$

$c = 1$

Now we know the equation is $y = mx + 1$.

Using the point (2, 2), we can substitute $x = 2$ and $y = 2$ into the equation:

$2 = m(2) + 1$

$2 = 2m + 1$

$2 - 1 = 2m$

$1 = 2m$

$m = \frac{1}{2}$

So the equation is $y = \frac{1}{2}x + 1$.

Now we want to find the value of $x$ when $y = 5$. Substituting $y = 5$ into the equation gives:

$5 = \frac{1}{2}x + 1$

$5 - 1 = \frac{1}{2}x$

$4 = \frac{1}{2}x$

$x = 4 \times 2$

$x = 8$

3. Final Answer

The value of $x$ when $y = 5$ is

8.