Question: the point $(-3,6)$ is on a line with a slope of $4$. find two more points on the line
1. **State the problem:** We are given a point $(-3,6)$ on a line with slope $4$, and we need to find two more points on this line.
2. **Recall the formula:** The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$ where $m$ is the slope.
3. **Use the point-slope form:** The equation of the line can be written as $$y - y_1 = m(x - x_1)$$ where $(x_1,y_1)$ is a known point.
4. **Plug in the known values:** $$y - 6 = 4(x + 3)$$
5. **Simplify the equation:** $$y - 6 = 4x + 12$$
$$y = 4x + 18$$
6. **Find two more points:** Choose two values for $x$ and find corresponding $y$.
- For $x = 0$: $$y = 4(0) + 18 = 18$$ so point is $(0,18)$.
- For $x = 1$: $$y = 4(1) + 18 = 22$$ so point is $(1,22)$.
**Final answer:** Two more points on the line are $(0,18)$ and $(1,22)$.