To solve the equation $y = x - 5$ by graphing, follow these steps:

1. Identify the equation:

The equation is in the form $y = mx + b$, which is the slope-intercept form, where:

• $m$ is the slope of the line (the rate at which $y$ changes with respect to $x$),
• $b$ is the y-intercept (the point where the line crosses the y-axis).

In this case:

• $m = 1$ (because the coefficient of $x$ is 1),
• $b = -5$ (because the constant is -5).

2. Plot the y-intercept:

Start by plotting the y-intercept at $(0, -5)$. This is where the line crosses the y-axis.

3. Use the slope to find another point:

The slope $m = 1$ means that for every 1 unit increase in $x$, $y$ increases by 1. Starting from $(0, -5)$:

• If $x = 1$, then $y = 1 - 5 = -4$, so plot the point $(1, -4)$.

4. Draw the line:

Once you have at least two points, draw a straight line through them. This line is the graph of $y = x - 5$.

Conclusion:

The graph of the equation will be a straight line that passes through $(0, -5)$ and $(1, -4)$ and extends infinitely in both directions.

Would you like me to show you a visual representation of this graph?