Subjects algebra

Parallel Line 37171B

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1. **State the problem:** Find the equation of line W that passes through the point $(2, 11)$ and is parallel to the line $y = 4x + 5$. 2. **Recall the formula:** The general form of a line is $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept. 3. **Important rule:** Parallel lines have the same slope. Since the given line has slope $m = 4$, line W also has slope $m = 4$. 4. **Use the point-slope form:** To find $c$, plug the point $(2, 11)$ into $y = 4x + c$: $$11 = 4 \times 2 + c$$ 5. **Solve for $c$:** $$11 = 8 + c$$ $$c = 11 - 8$$ $$c = 3$$ 6. **Write the equation of line W:** $$y = 4x + 3$$ **Final answer:** The equation of line W is $y = 4x + 3$.