Question: Write the equation of the line in fully simplified slope-intercept form.
Graph: a rising straight line passes through points $(0, -2)$, $(1, 0)$, $(2, 2)$, $(3, 4)$, $(4, 6)$, $(5, 8)$, $(6, 10)$, with arrows extending to the bottom-left and top-right; position_hint = center.
1. **State the problem:** Find the equation of the line passing through the points given, in slope-intercept form $y=mx+b$.
2. **Identify points:** We have points $(0,-2)$ and $(1,0)$ among others.
3. **Calculate the slope $m$:**
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{1 - 0} = \frac{2}{1} = 2$$
4. **Use slope-intercept form $y=mx+b$:**
Substitute $m=2$ and use point $(0,-2)$ to find $b$:
$$-2 = 2 \times 0 + b \implies b = -2$$
5. **Write the equation:**
$$y = 2x - 2$$
6. **Verify with another point:** For $(2,2)$:
$$y = 2(2) - 2 = 4 - 2 = 2$$ which matches the point.
**Final answer:**
$$\boxed{y = 2x - 2}$$