Question

find the equation and slope of a line that is perpendicular to the x-axis and passes through the point (-5, 3). click on \undefined\ as the answer if necessary.
equation:
slope:

Explanation:

Step1: Analyze the line's orientation

A line perpendicular to the x - axis is a vertical line. For a vertical line, the x - coordinate of all points on the line is the same.

Step2: Determine the equation of the line

The line passes through the point \((-5,3)\). Since it is a vertical line, the equation of the line is \(x=-5\) (because for all points on this vertical line, the x - value is - 5).

Step3: Determine the slope of the line

The slope of a line is given by the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). For a vertical line, the x - coordinates of any two points on the line are the same (\(x_2=x_1\)), so the denominator \(x_2 - x_1 = 0\). Division by zero is undefined, so the slope of a vertical line is undefined.

Answer:

Equation: \(x = - 5\)
Slope: Undefined