Graph each equation. 2x +5y = 20

Key Concepts

Linear Equations

A linear equation is an algebraic expression that represents a straight line when graphed on a coordinate plane. It typically takes the form Ax + By = C, where A, B, and C are constants. The solutions to a linear equation are the points (x, y) that satisfy the equation, and the graph of the equation shows all these solutions.

Slope-Intercept Form

The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope of the line and b represents the y-intercept. This form is particularly useful for quickly identifying the slope and y-intercept, allowing for easier graphing. Converting a standard form equation, like 2x + 5y = 20, into slope-intercept form can simplify the graphing process.

Graphing Linear Equations

Graphing a linear equation involves plotting points that satisfy the equation on a coordinate plane and connecting them to form a straight line. To graph the equation 2x + 5y = 20, one can find the x-intercept and y-intercept or convert it to slope-intercept form. Understanding how to plot these points accurately is essential for visualizing the relationship between the variables.