91Ó°ÊÓ

To start graphing a linear equation, first, you need to plot points on the coordinate graph. Points are determined by their x and y values.
For the equation given in the exercise, start with expressing y in terms of x, which was done in step 1: \( y = x + 1 \).
Choose values for x and then compute the corresponding y values as shown in the exercise. For instance: when \( x = -2 \), substituting into \( y = x + 1 \) yields \( y = -1 \).
This forms the point \((-2, -1)\). Repeat this step for other x values: \( x = 0 \) results in \( y = 1 \) forming the point \((0, 1)\), and \( x = 2 \) gives \( y = 3 \) forming the point \((2, 3)\).

• Select different values of x
• Use the equation to find corresponding y values
• Mark these points on the graph as pairs (x, y)

Plot these points accurately before proceeding to the next step.

The coordinate graph, also called the Cartesian plane, consists of a horizontal x-axis and a vertical y-axis. Each point on this plane is identified by an ordered pair \((x, y)\).
This system makes it easy to visualize the relationship between x and y.
After determining the points to plot (as we did in the earlier section), you place them on this coordinate graph.
Let's take the points calculated previously:

• \((-2, -1)\)
• \((0, 1)\)
• \((2, 3)\)

Find each corresponding x and y value on the axes and plot these points. Use a ruler to connect the points once plotted – you should see that they form a straight line. This line represents the linear equation you started with.
A few tips:

• Always label your axes
• Ensure scales for x and y are equal in size
• Double-check point placements for accuracy

A table of values is a useful tool when learning to plot linear equations. It's a simple chart that helps you organize and compute points that satisfy the equation.
Creating a table of values for the equation \( y = x + 1 \), involves selecting x values, computing y values, and listing their pairings. Here's how:

• Choose a few values for x, for instance, -2, 0, and 2
• Substitute these values into the equation to find the corresponding y
• Record these (x, y) pairs in the table

For example:

• When \( x = -2 \), \( y = -1 \)
• When \( x = 0 \), \( y = 1 \)
• When \( x = 2 \), \( y = 3 \)

Now, these values from your table will guide you in plotting points on the coordinate graph accurately. This structured approach not only helps in plotting but also ensures a clear understanding of how each point connects to the given equation.
Practice creating and using these tables to become more comfortable with graph plotting.