For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. through (2, -10), perpendicular to a line with undefined slope.

Key Concepts

Slope-Intercept Form

The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope of the line and b is the y-intercept. This form is particularly useful for quickly identifying the slope and y-intercept, making it easier to graph the line. In the context of the given question, converting the equation to this form will help visualize the line's position relative to the point (2, -10).

Standard Form

The standard form of a linear equation is written as Ax + By = C, where A, B, and C are integers, and A should be non-negative. This form is beneficial for solving systems of equations and understanding the relationship between the coefficients and the line's characteristics. In this question, converting the slope-intercept form to standard form will provide an alternative representation of the same line.

Perpendicular Lines

Two lines are perpendicular if the product of their slopes is -1. A line with an undefined slope is vertical, meaning its slope is infinite. Therefore, a line that is perpendicular to a vertical line must be horizontal, which has a slope of 0. Understanding this relationship is crucial for determining the correct slope for the line that passes through the point (2, -10) in the given problem.