Parallel Line 90D39A

1. **State the problem:** Find the equation of the line passing through the point $(-2, 1)$ and parallel to the line $y= \frac{4}{3} x + 7$. 2. **Recall the formula for a line parallel to another:** Lines that are parallel have the same slope. 3. **Identify the slope of the given line:** The slope $m$ of the line $y= \frac{4}{3} x + 7$ is $\frac{4}{3}$. 4. **Use point-slope form:** The equation of a line with slope $m$ passing through point $(x_1, y_1)$ is $$y - y_1 = m(x - x_1)$$ 5. **Substitute the known values:** $m = \frac{4}{3}$, $x_1 = -2$, $y_1 = 1$ $$y - 1 = \frac{4}{3} (x - (-2))$$ which simplifies to $$y - 1 = \frac{4}{3} (x + 2)$$ 6. **Check the options:** The correct equation is $$(y - 1) = \frac{4}{3} (x + 2)$$ **Final answer:** $(y - 1) = \frac{4}{3} (x + 2)$