For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. through (3, -5), parallel to y=4

The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope and b is the y-intercept. This form is useful for quickly identifying the slope of the line and where it crosses the y-axis. To write an equation in this form, one must know the slope and a point on the line.

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 solving systems of equations and analyzing the relationship between variables. Converting from slope-intercept to standard form often involves rearranging the equation.

Parallel lines have the same slope but different y-intercepts, meaning they will never intersect. When writing the equation of a line parallel to a given line, one must use the same slope as the original line. In this case, since the line y = 4 is horizontal, its slope is 0, which will be used to find the equation of the new line through the point (3, -5).