The given equation is $y = -x + 4$, which is a linear equation in slope-intercept form ($y = mx + b$), where:

• $m = -1$ is the slope.
• $b = 4$ is the y-intercept.

Finding the Intercepts:

1. Y-intercept: The y-intercept occurs when $x = 0$. Substituting $x = 0$ into the equation: $y = -(0) + 4 = 4$ So, the y-intercept is $(0, 4)$.

2. X-intercept: The x-intercept occurs when $y = 0$. Setting $y = 0$ in the equation: $0 = -x + 4$ Solving for $x$: $x = 4$ So, the x-intercept is $(4, 0)$.

Summary:

• X-intercept: $(4, 0)$
• Y-intercept: $(0, 4)$

Now you can graph the line by plotting these two intercepts and drawing a straight line through them.

Do you want more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How do you calculate the slope of a line between two points?
2. What is the general formula for slope-intercept form?
3. How does changing the slope $m$ affect the graph of the line?
4. What is the significance of the y-intercept in real-world applications?
5. How would the graph change if the equation were $y = -2x + 4$?

Tip: Always check your intercepts by substituting them back into the original equation to verify their correctness.