Complete the table of values for the equation and graph the...

Key Concepts

Graphing on the Coordinate Plane

Graphing involves plotting points on a coordinate plane using the x and y values and then connecting these points to visualize the relationship represented by the equation. For linear equations, drawing a straight line through the plotted points demonstrates the consistency of the relationship and helps in understanding concepts like slope and intercept.

Table of Values

A table of values is a systematic way of organizing selected pairs of x and y coordinates that satisfy the equation of a graph. By substituting chosen x values into the equation, the corresponding y values are computed to produce points that can be plotted on the coordinate plane. This method is especially helpful in graphing linear equations and verifying their properties.

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. It represents a straight line when graphed on a coordinate plane, and its general form can be expressed as y = mx + b, where m is the slope and b is the y-intercept.

Slope-Intercept Form

The slope-intercept form of a linear equation is given by y = mx + b. In this form, 'm' represents the slope of the line, indicating its steepness and direction, while 'b' is the y-intercept, the point where the line crosses the y-axis. This form is particularly useful for quickly graphing the equation and understanding how changes in the slope and intercept affect the line.

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