Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. m=5, b=15

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 format allows for easy identification of the line's steepness and where it crosses the y-axis. For example, if m = 5 and b = 15, the equation would be y = 5x + 15.

Standard Form

The standard form of a linear equation is typically written as Ax + By = C, where A, B, and C are integers, and A should be non-negative. This form is useful for quickly identifying intercepts and is often used in systems of equations. To convert from slope-intercept to standard form, rearranging the equation is necessary.

Linear Equations

Linear equations represent relationships with a constant rate of change, forming straight lines when graphed. They can be expressed in various forms, including slope-intercept and standard form. Understanding the characteristics of linear equations, such as slope and intercepts, is essential for graphing and solving problems involving these equations.