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

and are perpendicular to each other.

Step-by-step explanation:

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

, (Eq. 1)

Where:

- Dependent variable, dimensionless.

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

(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:

, (Eq. 2)

Where:

- Independent variable, dimensionless.

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

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

(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:

(Eq. 3)

Where and are the slopes of each line. It is quite evident that if , corresponding to a horizontal line, then becomes undefined, corresponding to a vertical line.

In consequence, we come to the conclusion that and are perpendicular to each other.

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step-by-step explanation: