Question 20 Pause Zoom Two lines are graph on a coordinate plane. The equation of the first line is \( 4 x+4 y=1 \) and the equation of the second line is \( x+y=-8 \). Which staternent about the two lines is true? A. The lines are parallel. B. The lines are the same line. C. The lines are perpendicular. D. Both lines intersect at point \( (0,-8) \).

Let's analyze the two given lines: 1. **First Line:** \( 4x + 4y = 1 \) - To find the slope, rewrite the equation in slope-intercept form (\( y = mx + b \)): \[ 4y = -4x + 1 \implies y = -x + \frac{1}{4} \] - **Slope (m₁):** \(-1\) 2. **Second Line:** \( x + y = -8 \) - Similarly, rewrite in slope-intercept form: \[ y = -x - 8 \] - **Slope (m₂):** \(-1\) **Comparing the Slopes:** - Both lines have the same slope (\(-1\)), which means they are **parallel**. **Checking for Coincidence:** - For the lines to be the same, their y-intercepts must also be equal. - The first line has a y-intercept of \(\frac{1}{4}\), while the second line has a y-intercept of \(-8\). - Since the y-intercepts are different, the lines are **distinct** and not the same line. **Option D: Intersection at (0, -8):** - Substitute \((0, -8)\) into both equations: - First Line: \(4(0) + 4(-8) = -32 \neq 1\) ❌ - Second Line: \(0 + (-8) = -8\) ✅ - The point \((0, -8)\) only lies on the second line, not on the first. **Conclusion:** The two lines are **parallel** but not the same. **Answer:** A. The lines are parallel.