Write an equation for each line described. Give answers in standard form for Exercises 11-20 and

step 1 This problem is looking for the equation of a line that passes through the point negative 3 and

Write an equation for each line described. Give answers in...

Key Concepts

Standard Form

Standard form for a linear equation is typically written as Ax + By = C, where A, B, and C are integers and A is non-negative. This form is useful for certain types of algebraic manipulations and comparisons between lines.

Slope-Intercept Form

Slope-intercept form is one way to write the equation of a line, expressed as y = mx + b, where m is the slope and b is the y-intercept. This form is especially useful for quickly identifying both the slope of the line and the point where it crosses the y-axis.

Horizontal Line

A horizontal line is a line where every point on the line has the same y-coordinate. Its slope is 0, and its equation can be simplified to y = k for some constant k, representing its constant vertical position on the coordinate plane.

Linear Equation

A linear equation represents a straight line on a coordinate plane and can be expressed in various forms. It expresses the relationship between x and y, usually with constant coefficients, so that the graph of the equation is a line. This concept underlies finding equations that match given geometric properties such as slopes and intercepts.

Slope

The slope of a line is a measure of its steepness and direction, calculated as the ratio of the change in y to the change in x. A slope of 0 indicates that the line is horizontal, meaning there is no vertical change as you move along the line.

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