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 that a vertical line has an undefined slope and is represented by the equation x = a constant.
2. Recognize that the line passes through the point (-6, 4).
3. Since the line is vertical, the x-coordinate of every point on the line is the same.
4. Set the equation of the line to x = -6, as the x-coordinate of the given point is -6.
5. Conclude that the equation of the vertical line through (-6, 4) is x = -6.

Key Concepts

Vertical Lines

A vertical line is defined as a line that runs up and down the page and has an undefined slope. The equation of a vertical line can be expressed in the form x = a, where 'a' is the x-coordinate of any point on the line. For example, a vertical line passing through the point (-6, 4) would be represented by the equation x = -6.

Standard Form of a Line

The standard form of a linear equation is typically written as Ax + By = C, where A, B, and C are integers, and A should be non-negative. This form is useful for quickly identifying the x-intercept and y-intercept of the line. For vertical lines, the standard form is simply x = a, which fits the criteria of the standard form with B = 0.

Slope-Intercept Form

The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope and b is the y-intercept. This form is particularly useful for graphing because it directly provides the slope and where the line crosses the y-axis. However, vertical lines cannot be expressed in this form since they do not have a defined slope, making it impossible to represent them as y = mx + b.