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)

Verified step by step guidance

1. 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.
2. 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.
3. Since the line passes through the point \((-7, 4)\), the y-value for every point on the line is 4.
4. Write the equation of the line as \(y = 4\).
5. 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$.

Key Concepts

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.