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

Verified step by step guidance

1. <insert step 1: Identify the equation to be graphed, which is y = x + 2. This is a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept.>
2. <insert step 2: Determine the slope (m) and y-intercept (b) from the equation. Here, m = 1 and b = 2.>
3. <insert step 3: Create a table of values using the given x-values: -3, -2, -1, 0, 1, 2, 3. For each x-value, substitute it into the equation to find the corresponding y-value.>
4. <insert step 4: Plot the points (x, y) on a coordinate plane using the values from the table.>
5. <insert step 5: Draw a straight line through the plotted points, extending it in both directions, to represent the graph of the equation y = x + 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. In the given equation y = x + 2, the slope is 1, indicating that for every unit increase in x, y increases by the same amount.

Graphing Points

Graphing points involves plotting specific coordinates on a Cartesian plane, where the x-coordinate represents the horizontal position and the y-coordinate represents the vertical position. For the equation y = x + 2, you can calculate y for each given x value (-3, -2, -1, 0, 1, 2, 3) to find corresponding points, which can then be plotted to visualize the linear relationship.

Slope-Intercept Form

The slope-intercept form of a linear equation is expressed as y = mx + b, where m is the slope and b is the y-intercept. This form is particularly useful for quickly identifying the slope and y-intercept of a line, allowing for easy graphing. In the equation y = x + 2, the slope is 1 and the y-intercept is 2, indicating that the line crosses the y-axis at (0, 2).