Question: An equation and two ordered pairs are given. Show that each pair is a solution to the equation. Then use the graph of the two points to determine another solution.
yequalsxminus1; (0, negative 1) and (1, 0)
1. **State the problem:**
We are given the equation $$y = x - 1$$ and two ordered pairs: $$(0, -1)$$ and $$(1, 0)$$.
We need to check if each pair is a solution to the equation and then find another solution using the graph.
2. **Check if $$(0, -1)$$ is a solution:**
Substitute $x=0$ into the equation:
$$y = 0 - 1 = -1$$
The $y$-value from the pair is $-1$, which matches the equation.
3. **Check if $$(1, 0)$$ is a solution:**
Substitute $x=1$ into the equation:
$$y = 1 - 1 = 0$$
The $y$-value from the pair is $0$, which matches the equation.
4. **Graph the equation and points:**
The equation $$y = x - 1$$ is a straight line with slope $1$ and $y$-intercept $-1$.
The points $$(0, -1)$$ and $$(1, 0)$$ lie on this line.
5. **Find another solution using the graph:**
Choose $x = -2$ and substitute into the equation:
$$y = -2 - 1 = -3$$
So the point $$(-2, -3)$$ lies on the line.
6. **Check if $(-2, -3)$ is a solution:**
Substitute $x = -2$:
$$y = -2 - 1 = -3$$
The $y$-value matches, so $$(-2, -3)$$ is a solution.
**Final answers:**
- $$(0, -1)$$ is a solution.
- $$(1, 0)$$ is a solution.
- $(-2, -3)$$ is also a solution found from the graph.