Complete the table of values and graph each equation. y=-2...

Key Concepts

Graphing Linear Equations

Graphing a linear equation involves plotting key points determined from the equation (often through a table of values), connecting those points with a straight line, and analyzing features like slope and intercepts to understand the behavior of the line.

Linear Equation

A linear equation represents a straight line when graphed. It features a constant rate of change and is typically written in the form y = mx + b, where m is the slope and b is the y-intercept.

Slope-Intercept Form

This form, given by y = mx + b, clearly shows the slope (m) and the y-intercept (b) of a linear equation. It makes it easy to graph a line by starting at the y-intercept and using the slope to determine the direction and steepness of the line.

Slope

The slope of a line is a measure of its steepness and direction. It is calculated as the change in the y-value divided by the change in the x-value, indicating how much y increases or decreases as x changes.

Y-Intercept

The y-intercept is the point where the line crosses the y-axis, which occurs when x is zero. It provides a starting point for graphing the line and is a key component of the slope-intercept form.

Table of Values

A table of values is a systematic way to evaluate a function at specific x-values. By substituting chosen x-values into the linear equation, corresponding y-values are obtained, which can then be plotted on a coordinate grid to form the graph of the equation.

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