Find the general form of the equation of the line that...

Find the general form of the equation of the line that passes through the given point and has the indicated slope. Sketch the line by hand. Use a graphing utility to verify your sketch, if possible.
Point $\quad$ Slope
$(0,-2) \quad m=3$

Key Concepts

Point-Slope Form

The point-slope form is a method for writing the equation of a line when a point on the line and its slope are known. It is expressed as y - y? = m(x - x?), where (x?, y?) is the given point and m is the slope. This form is particularly useful for quickly deriving the equation of a line from minimal information.

General Form of a Linear Equation

The general form of a linear equation is typically written as Ax + By + C = 0, where A, B, and C are constants. It is a standard way to represent a line that can be converted from other forms, such as the point-slope or slope-intercept forms, by rearranging and combining like terms. This form is useful in various applications including solving systems of equations and analyzing geometric properties.

Linear Equations

A linear equation represents a straight line in a coordinate plane and is characterized by a constant rate of change (slope) and a constant term (y-intercept when in slope-intercept form). It can be expressed in several forms, such as the slope-intercept form, point-slope form, and general form, each highlighting different properties of the line.

Slope

The slope of a line measures its steepness or incline and is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. It is a crucial concept as it determines the line’s direction and how quickly it rises or falls across the coordinate plane.

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