Question: Find the x and y intercepts
of this linear equation.
−x + y = 3
x-intercept ([?], )
y-intercept ( , )
1. **State the problem:** Find the x-intercept and y-intercept of the linear equation $$-x + y = 3$$.
2. **Recall the intercept definitions:**
- The x-intercept is the point where the line crosses the x-axis, so $$y=0$$.
- The y-intercept is the point where the line crosses the y-axis, so $$x=0$$.
3. **Find the x-intercept:**
Set $$y=0$$ in the equation:
$$-x + 0 = 3$$
$$-x = 3$$
Multiply both sides by $$-1$$:
$$\cancel{-1} \times -x = \cancel{-1} \times 3$$
$$x = -3$$
So the x-intercept is $$(-3, 0)$$.
4. **Find the y-intercept:**
Set $$x=0$$ in the equation:
$$-0 + y = 3$$
$$y = 3$$
So the y-intercept is $$(0, 3)$$.
**Final answer:**
- x-intercept: $$(-3, 0)$$
- y-intercept: $$(0, 3)$$