Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (1, 6), perpendicular to 3x+5y=1

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 an equation into standard form, you may need to rearrange terms and eliminate fractions.

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 convert between forms is essential for solving problems involving lines.

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 problem, you first need to determine the slope of the given line and then use this relationship to find the slope of the line that is perpendicular to it.