1. **State the problem:** We have a line $k$ that intersects the y-axis at $(0, -6)$ and passes through $(2, 2)$. We need to find the value of $w$ for the point $(20, w)$ on the same line. 2. **Formula and rules:** The equation of a line in slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Find the slope $m$:** The slope is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using points $(0, -6)$ and $(2, 2)$: $$m = \frac{2 - (-6)}{2 - 0} = \frac{8}{2} = 4$$ 4. **Write the line equation:** Since the y-intercept $b = -6$, the line equation is: $$y = 4x - 6$$ 5. **Find $w$ when $x=20$:** Substitute $x=20$ into the equation: $$w = 4(20) - 6 = 80 - 6 = 74$$ **Final answer:** $w = 74$