Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (5,-8), m = 0

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Identify the given information: the line passes through the point (5, -8) and has a slope m = 0.

Recall that a slope of 0 means the line is horizontal, so the equation of the line will be of the form \(y = b\), where \(b\) is a constant.

Since the line passes through (5, -8), substitute \(x = 5\) and \(y = -8\) into the equation \(y = b\) to find \(b\).

This gives \(-8 = b\), so the equation of the line is \(y = -8\).

To write the equation in standard form, rearrange \(y = -8\) to \(0x + 1y = -8\), which is \(y = -8\) in standard form.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equation of a Line

An equation of a line represents all points that lie on that line. Common forms include slope-intercept form (y = mx + b) and standard form (Ax + By = C). Understanding how to write these equations from given information is fundamental in algebra.

Slope of a Line

Slope (m) measures the steepness and direction of a line. A slope of 0 means the line is horizontal, so the y-value remains constant for all x-values. Recognizing slope helps in writing the correct equation for the line.

Forms of Linear Equations

Standard form (Ax + By = C) and slope-intercept form (y = mx + b) are two common ways to express linear equations. Standard form is often used for integer coefficients, while slope-intercept form clearly shows slope and y-intercept, aiding graphing and interpretation.

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