For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. through (0, 5), perpendicular to 8x+5y=3

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 useful for quickly identifying the slope and y-intercept, making it easier to graph the line. To convert an equation into this form, one typically solves for y.

Standard Form

The standard form of a linear equation is given by Ax + By = C, where A, B, and C are integers, and A should be non-negative. This form is beneficial for analyzing the relationship between x and y and is often used in systems of equations. To convert from slope-intercept form to standard form, rearranging the equation is necessary.

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. Understanding this concept is crucial for finding the slope of the line that is perpendicular to a given line, which is necessary for solving the problem at hand.