Graph each equation in Exercises 1–4. Let x= -3, -2. -1, 0, 1, 2 and 3. y = 2x-2

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 y = mx + b, where m is the slope and b is the y-intercept. Understanding linear equations is essential for graphing, as it allows you to determine how changes in x affect the value of y.

Slope and Y-Intercept

The slope of a line indicates its steepness and direction, calculated as the change in y over the change in x (rise/run). The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero. In the equation y = 2x - 2, the slope is 2 and the y-intercept is -2, which are crucial for accurately plotting the graph.

Graphing Points

Graphing points involves plotting specific (x, y) coordinates on a Cartesian plane. For the equation y = 2x - 2, you will substitute the given x values (-3, -2, -1, 0, 1, 2, 3) to find corresponding y values. This process helps visualize the relationship between x and y, forming the linear graph of the equation.