1. **State the problem:** We need to find the equation of the linear function in slope-intercept form $y=mx+b$ that fits the points given in the table: $(-1,0)$, $(1,4)$, $(3,8)$, and $(5,12)$. 2. **Recall the formula:** The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by: $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ The slope-intercept form is: $$y=mx+b$$ where $b$ is the y-intercept. 3. **Calculate the slope $m$ using points $(-1,0)$ and $(1,4)$:** $$m=\frac{4 - 0}{1 - (-1)}=\frac{4}{2}=2$$ 4. **Use the slope and one point to find $b$:** Using point $(-1,0)$: $$0=2(-1)+b$$ $$0=-2+b$$ $$b=2$$ 5. **Write the equation:** $$y=2x+2$$ 6. **Verify with another point $(3,8)$:** $$y=2(3)+2=6+2=8$$ which matches the table. **Final answer:** $$y=2x+2$$