Questions: The equation of a line is given below. Find the slope of a line that is a. parallel to the line with the given equation, and b. perpendicular to the line with the given equation. y=-11 x a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. A line parallel to the given line has slope -11. (Simplify your answer.) B. The slope is undefined. b. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. A line perpendicular to the given line has slope (Simplify your answer.) B. The slope is undefined.

Solution Steps

The equation of the line is given as: \[ y = -11x \] This is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. From the equation, we can see that the slope \( m \) is: \[ m = -11 \]

Parallel lines have the same slope. Therefore, the slope of a line parallel to the given line is the same as the slope of the given line: \[ \text{Slope of parallel line} = -11 \] Thus, the correct choice for part (a) is: \[ \text{A. A line parallel to the given line has slope } -11. \]

Perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of \( -11 \) is: \[ \text{Slope of perpendicular line} = \frac{1}{11} \] Thus, the correct choice for part (b) is: \[ \text{A. A line perpendicular to the given line has slope } \frac{1}{11}. \]

Final Answer