Line Equation Baffd6
1. **State the problem:** We need to find the equation of the line shown on the graph in slope-intercept form, which is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept.
2. **Identify two points on the line:** From the description, the line passes near $(-8, 8)$ and $(8, 0)$.
3. **Calculate the slope $m$:**
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 8}{8 - (-8)} = \frac{-8}{16} = -\frac{1}{2}$$
4. **Find the y-intercept $b$:** Use the slope and one point, for example $(-8, 8)$:
$$8 = -\frac{1}{2} \times (-8) + b$$
$$8 = 4 + b$$
$$b = 8 - 4 = 4$$
5. **Write the equation:**
$$y = -\frac{1}{2}x + 4$$
This is the slope-intercept form of the line.