Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = -(1/2)x

Verified step by step guidance

1. Start by understanding the equation y = -(1/2)x. This is a linear equation where the slope is -1/2 and the y-intercept is 0. The slope indicates that for every 1 unit increase in x, y decreases by 1/2.
2. Create a table of values for the given x-values: x = -3, -2, -1, 0, 1, 2, 3. For each x-value, substitute it into the equation y = -(1/2)x to calculate the corresponding y-value.
3. For example, when x = -3, substitute into the equation: y = -(1/2)(-3). Simplify to find the y-value. Repeat this process for all other x-values.
4. Once you have the table of x and y values, plot these points on a coordinate plane. Each point will have coordinates (x, y) based on your calculations.
5. After plotting all the points, draw a straight line through them. This line represents the graph of the equation y = -(1/2)x. Ensure the line extends in both directions and label the axes appropriately.

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 students to identify the relationship between the variables and predict the behavior of the line.

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, represented by the value of y when x is zero. In the equation y = -(1/2)x, the slope is -1/2, indicating a downward slope, and the y-intercept is 0, meaning the line passes through the origin.

Graphing Points

Graphing points involves plotting specific coordinates (x, y) on a Cartesian plane to visualize the relationship defined by an equation. For the equation y = -(1/2)x, substituting values for x (like -3, -2, -1, 0, 1, 2, 3) allows us to calculate corresponding y values, which can then be plotted to form the line. This process is crucial for understanding how changes in x affect y.