Question: Find the y-intercept and x-intercept of the line.
7x − y = 7
y-intercept:
x-intercept:
1. **State the problem:** We need to find the y-intercept and x-intercept of the line given by the equation $$7x - y = 7$$.
2. **Recall the definitions:**
- The y-intercept is the point where the line crosses the y-axis, so $$x=0$$.
- The x-intercept is the point where the line crosses the x-axis, so $$y=0$$.
3. **Find the y-intercept:**
- Substitute $$x=0$$ into the equation:
$$7(0) - y = 7$$
$$0 - y = 7$$
$$-y = 7$$
- Multiply both sides by $$-1$$:
$$\cancel{-}y \times \cancel{-}1 = 7 \times -1$$
$$y = -7$$
- So the y-intercept is at the point $$(0, -7)$$.
4. **Find the x-intercept:**
- Substitute $$y=0$$ into the equation:
$$7x - 0 = 7$$
$$7x = 7$$
- Divide both sides by $$7$$:
$$\frac{7x}{\cancel{7}} = \frac{7}{\cancel{7}}$$
$$x = 1$$
- So the x-intercept is at the point $$(1, 0)$$.
**Final answers:**
- Y-intercept: $$(0, -7)$$
- X-intercept: $$(1, 0)$$