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. horizontal, through (-7,4)

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Identify the type of line described: a horizontal line has a slope of 0, meaning it does not rise or fall as it moves along the x-axis.

Recall that the equation of a horizontal line is always of the form $y = k$, where $k$ is the constant y-value for all points on the line.

Since the line passes through the point $(-7, 4)$, the y-value for every point on the line is 4.

Write the equation of the line as $y = 4$.

Note that this equation is already in slope-intercept form $y = mx + b$ with $m = 0$ and $b = 4$, and it can also be considered in standard form as $0x + y = 4$.

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Key Concepts

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

Equation of a Horizontal Line

A horizontal line has a constant y-value for all x-values, meaning its slope is zero. The equation of a horizontal line is written as y = k, where k is the y-coordinate of any point on the line. For example, a horizontal line through (-7, 4) is y = 4.

Standard Form of a Linear Equation

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A ≥ 0. This form is useful for quickly identifying intercepts and is often required for certain exercises. For horizontal lines, the standard form is typically y = constant, which can be rewritten as 0x + 1y = constant.

Slope-Intercept Form of a Linear Equation

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. It clearly shows the slope and where the line crosses the y-axis. For horizontal lines, the slope m = 0, so the equation simplifies to y = b, making it easy to write and interpret.

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