Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (4, -4), perpendicular to x=4

Key Concepts

Standard Form of a Linear Equation

The standard form of a linear equation is expressed as Ax + By = C, where A, B, and C are integers, and A should be non-negative. This form is useful for easily identifying the x- and y-intercepts of the line. To convert a slope-intercept form equation (y = mx + b) to standard form, you can rearrange the terms to fit the Ax + By = C format.

Slope-Intercept Form

The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope of the line and b is the y-intercept. This form is particularly useful for quickly graphing the line, as it directly provides the slope and where the line crosses the y-axis. Understanding how to manipulate this form is essential for converting between different representations of linear equations.

Perpendicular Lines

Two lines are perpendicular if the product of their slopes is -1. This means that if one line has a slope of m, the slope of the line perpendicular to it will be -1/m. In this question, since the line x = 4 is vertical (undefined slope), the perpendicular line will be horizontal, which has a slope of 0. This concept is crucial for determining the correct slope when writing the equations.