The Point-Slope Form of the Equation of a Line In Exercises...

The Point-Slope Form of the Equation of a Line In Exercises 25-32, find an equation of the line that passes through the given point and has the indicated slope. Sketch the line by hand. Use a graphing utility to verify your sketch, if possible.
$(-10,4), \quad m$ is undefined

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Key Concepts

Equation of a Line

This concept involves finding a formula that represents all the points located on a straight line. The equation of a line typically relates the x and y coordinates and can be expressed in different forms such as slope-intercept, point-slope, or standard form.

Point-Slope Form

The point-slope form of a line is a method for writing the equation of a line when a point on the line and its slope are known. It is expressed as y - y? = m(x - x?), where (x?, y?) is a given point on the line and m is the slope.

Undefined Slope

An undefined slope occurs when the change in x is zero, meaning the line is vertical. In mathematical terms, division by zero is not allowed so the slope, given by m = ?y/?x, becomes undefined and indicates that all points on the line share the same x-coordinate.

Vertical Line

A vertical line is characterized by an equation of the form x = a constant value. Because its slope is undefined, the line does not have a y-intercept in the usual sense, and every point on the line has the same x-coordinate.

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