To graph the equation $y = x - 4$ using intercepts, we will find both the x-intercept and the y-intercept.

Step 1: Find the y-intercept

The y-intercept occurs when $x = 0$. Substitute $x = 0$ into the equation:

$y = 0 - 4 = -4$

So, the y-intercept is $(0, -4)$.

Step 2: Find the x-intercept

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

$0 = x - 4$

Solving for $x$:

$x = 4$

So, the x-intercept is $(4, 0)$.

Step 3: Plot the intercepts

Now you have two points:

• $(0, -4)$ (the y-intercept)
• $(4, 0)$ (the x-intercept)

Step 4: Draw the line

Plot these two points on the graph and draw a straight line through them. This line represents the equation $y = x - 4$.

Would you like a graph of this? Do you have any questions or need more details?

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Here are 5 related questions to expand on this:

1. How do we find the slope of the line from this equation?
2. What does the slope represent in the context of this graph?
3. How can you check if a point is on the line?
4. How does changing the equation to $y = x - 3$ affect the intercepts?
5. What are other methods to graph a linear equation?

Tip: For a linear equation in the form $y = mx + b$, $b$ represents the y-intercept.