1. **Problem Statement:** Identify the slope and y-intercept for each equation. 2. **Formula:** The slope-intercept form of a line is given by $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Rules:** - The slope $m$ is the coefficient of $x$. - The y-intercept $b$ is the constant term. 4. **Solutions:** - a) $y = x + 6$ - Slope $m = 1$ - Y-intercept $b = 6$ - b) $y = -3$ - This is a horizontal line, so slope $m = 0$ - Y-intercept $b = -3$ - c) $y = -\frac{3}{4}x$ - Slope $m = -\frac{3}{4}$ - Y-intercept $b = 0$ - d) $y = -x - 2$ - Slope $m = -1$ - Y-intercept $b = -2$ 5. **Calculating slope from points:** - Given points $(x_1, y_1) = (2, 4)$ and $(x_2, y_2) = (7, 10)$ - Slope formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ - Substitute values: $$m = \frac{10 - 4}{7 - 2} = \frac{6}{5}$$ **Final answers:** - a) Slope = 1, Y-intercept = 6 - b) Slope = 0, Y-intercept = -3 - c) Slope = $-\frac{3}{4}$, Y-intercept = 0 - d) Slope = -1, Y-intercept = -2 - Slope from points = $\frac{6}{5}$