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. vertical, through (-6, 4)

Verified step by step guidance

1. Identify the type of line described: a vertical line. Vertical lines have an undefined slope and are represented by equations of the form \(x = a\), where \(a\) is the x-coordinate of every point on the line.
2. Since the line passes through the point \((-6, 4)\), the x-coordinate for all points on this vertical line is \(-6\).
3. Write the equation of the vertical line using the x-coordinate from the given point: \(x = -6\).
4. Confirm that this equation is in standard form. For vertical lines, the standard form is typically written as \(x = a\), which is already the case here.
5. No further simplification is needed, and the equation \(x = -6\) fully describes the vertical line through \((-6, 4)\).

Key Concepts

Equation of a Vertical Line

A vertical line has an undefined slope and is represented by an equation of the form x = a, where a is the x-coordinate of every point on the line. For example, a vertical line through (-6, 4) is x = -6, meaning all points have x = -6 regardless of y.

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. Vertical lines can be written in this form by setting B = 0, such as x = -6 becoming 1x + 0y = -6.

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. Vertical lines cannot be expressed in this form because their slope is undefined, so only non-vertical lines can be written as y = mx + b.