To find the intercepts for the equation $y = -x + 4$:

1. Y-Intercept:

The y-intercept is the point where the line crosses the y-axis. This occurs when $x = 0$.

Given the equation: $y = -x + 4$ Substituting $x = 0$: $y = -(0) + 4 = 4$ So, the y-intercept is $(0, 4)$.

2. X-Intercept:

The x-intercept is the point where the line crosses the x-axis. This occurs when $y = 0$.

Set $y = 0$ in the equation: $0 = -x + 4$ Solve for $x$: $x = 4$ So, the x-intercept is $(4, 0)$.

Summary:

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

Would you like to explore anything else, or do you have additional questions?

Here are five related questions:

1. How do you find the intercepts for a quadratic equation?
2. What do the intercepts represent on a graph?
3. How would the intercepts change if the equation was $y = -2x + 4$?
4. Can a linear equation have more than one x-intercept?
5. How can you determine the slope if only the intercepts are given?

Tip: The intercepts can be found by setting $x = 0$ (for the y-intercept) and $y = 0$ (for the x-intercept) in the equation.