Question

Rewrite each equation in​ slope-intercept form, if necessary. Then determine whether the lines are perpendicular. x = 9 y = -1 Are the lines​ perpendicular?

Answer 1

Answer:

$x = 9$ and $y = -1$ are perpendicular to each other.

Step-by-step explanation:

From Analytical Geometry we know that horizontal lines are of the form:

$y = a$, $\forall \,a\in\mathbb{R}$ (Eq. 1)

Where:

$y$ - Dependent variable, dimensionless.

Which means that for all value of $x$ (independent variable) has $a$ as their image. If we write this equation in slope-intercept form, we get that:

$y = 0\cdot x + a$ (Eq. 1b)

Where slope is the ratio of the change in dependent variable to the change in independent variable.

Whereas vertical lines have the following one:

$x = b$, $\forall \,b\in\mathbb{R}$ (Eq. 2)

Where:

$x$ - Independent variable, dimensionless.

Which means that for all value of $y$ (dependent variable) has $b$ as their image.

If we write this equation in slope-intercept form, we get that:

$x = 0\cdot y + a$ (Eq. 2b)

Where slope is the ratio of the change in independent variable to the change in independent variable.

In addition, we must remember that two lines perpendicular to each other observe the following relation:

$m_{A} = -\frac{1}{m_{B}}$ (Eq. 3)

Where $m_{A}$ and $m_{B}$ are the slopes of each line. It is quite evident that if $m_{A} = 0$, corresponding to a horizontal line, then $m_{B}$ becomes undefined, corresponding to a vertical line.

In consequence, we come to the conclusion that $x = 9$ and $y = -1$ are perpendicular to each other.