Question: What is the equation of line H?
Give your answer in the form $y = mx + c$
Line H: a straight line on a coordinate grid, crossing the y-axis at 10 and passing through approximately $(2, 40)$, so the equation is $y = 15x + 10$.
1. **State the problem:** Find the equation of line H in the form $y = mx + c$.
2. **Identify given information:** The line crosses the y-axis at $10$, so $c = 10$.
3. **Use the point-slope form:** The line passes through the point $(2, 40)$.
4. **Calculate the slope $m$:**
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{40 - 10}{2 - 0} = \frac{30}{2} = 15$$
5. **Write the equation:**
$$y = 15x + 10$$
6. **Explanation:** The slope $m$ tells us how steep the line is, and $c$ is where the line crosses the y-axis. Using the point and y-intercept, we found $m = 15$ and $c = 10$, so the equation is $y = 15x + 10$.