which statement is true about the graphs of the two lines y = -6 and x = 1/6?\nthe lines are perpendicular…

which statement is true about the graphs of the two lines y = -6 and x = 1/6?\nthe lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope that is undefined, and the graph of x = 1/6 is a vertical line with a slope of 0.\nthe lines are perpendicular to each other because the graph of y = -6 is a vertical line with a slope that is undefined, and the graph of x = 1/6 is a horizontal line with a slope of 0.\nthe lines are perpendicular to each other because the graph of y = -6 is a vertical line with a slope of 0, and the graph of x = 1/6 is a horizontal line with a slope that is undefined.\nthe lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope of 0, and the graph of x = 1/6 is a vertical line with a slope that is undefined.

which statement is true about the graphs of the two lines y = -6 and x = 1/6?\nthe lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope that is undefined, and the graph of x = 1/6 is a vertical line with a slope of 0.\nthe lines are perpendicular to each other because the graph of y = -6 is a vertical line with a slope that is undefined, and the graph of x = 1/6 is a horizontal line with a slope of 0.\nthe lines are perpendicular to each other because the graph of y = -6 is a vertical line with a slope of 0, and the graph of x = 1/6 is a horizontal line with a slope that is undefined.\nthe lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope of 0, and the graph of x = 1/6 is a vertical line with a slope that is undefined.

Answer

Answer:

D. The lines are perpendicular to each other because the graph of $y = - 6$ is a horizontal line with a slope of 0, and the graph of $x=\frac{1}{6}$ is a vertical line with a slope that is undefined.

Explanation:

Step1: Analyze the line $y=-6$

The equation $y = - 6$ represents a horizontal line. For a horizontal line, the change in the $y$ - value ($\Delta y$) between any two points on the line is 0. Using the slope formula $m=\frac{\Delta y}{\Delta x}$, when $\Delta y = 0$, the slope $m = 0$.

Step2: Analyze the line $x=\frac{1}{6}$

The equation $x=\frac{1}{6}$ represents a vertical line. For a vertical line, the change in the $x$ - value ($\Delta x$) between any two points on the line is 0. Using the slope formula $m=\frac{\Delta y}{\Delta x}$, when $\Delta x = 0$, the slope is undefined since division by zero is not allowed in mathematics.

Step3: Determine the relationship between the lines

A horizontal line and a vertical line are perpendicular to each other. So, the line $y=-6$ (horizontal with slope 0) and the line $x = \frac{1}{6}$ (vertical with undefined slope) are perpendicular.