1. **State the problem:** We are given two sets of points and need to find the equations of the lines they represent. 2. **Identify the points:** - First set: $(-1,2), (0,1), (1,0), (2,-1), (3,-2)$ - Second set: $(-2,0), (-1,1), (0,2), (1,3), (2,4)$ 3. **Recall the formula for a line:** The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 4. **Calculate the slope $m$ for the first set:** Choose two points, for example $(-1,2)$ and $(0,1)$: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 2}{0 - (-1)} = \frac{-1}{1} = -1$$ 5. **Find the y-intercept $b$ for the first set:** Use point $(0,1)$ where $x=0$, so $b = y = 1$. 6. **Write the equation for the first set:** $$y = -1 \cdot x + 1 = -x + 1$$ 7. **Calculate the slope $m$ for the second set:** Choose two points, for example $(-2,0)$ and $(-1,1)$: $$m = \frac{1 - 0}{-1 - (-2)} = \frac{1}{1} = 1$$ 8. **Find the y-intercept $b$ for the second set:** Use point $(0,2)$ where $x=0$, so $b = y = 2$. 9. **Write the equation for the second set:** $$y = 1 \cdot x + 2 = x + 2$$ **Final answers:** - First line: $y = -x + 1$ - Second line: $y = x + 2$