Graphing the Linear Equation y - 7 -x

When it comes to graphing a linear equation, the goal is to visualize the relationship between the variables x and y. In this article, we will walk through the process of graphing the linear equation y - 7 -x. This equation can be transformed into a more recognizable form, and then we will use a step-by-step approach to plot the line.

Step 1: Transform the Equation into Slope-Intercept Form

The first step is to rewrite the given equation in the slope-intercept form, y mx b. This form allows us to easily identify the slope (m) and the y-intercept (b).

y - 7 -x
To isolate y, we add 7 to both sides of the equation:

y -x 7

Now, the equation is in the slope-intercept form, where the slope (m) is -1 and the y-intercept (b) is 7.

Step 2: Identify the Y-Intercept

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of y when x 0. In our equation, the y-intercept is 7. Therefore, we know that the line passes through the point (0, 7).

Step 3: Create a Table of Values

Next, we create a table of values by substituting different values of x into the equation to find the corresponding y-values.

x y -3 10 -2 9 -1 8 0 7 1 6 2 5 3 4

Using this table, we can determine several points on the line:

(-3, 10), (-2, 9), (-1, 8), (0, 7), (1, 6), (2, 5), (3, 4)

Step 4: Plot the Points and Draw the Line

Now that we have the y-intercept and several other points on the line, we can plot these points on a graph and connect them to form the line.

Here is the step-by-step process:

Draw the x- and y-axes on a graph paper. Mark the y-intercept point (0, 7) on the y-axis. Plot the other points from the table: (-3, 10), (-2, 9), (-1, 8), (1, 6), (2, 5), (3, 4). Connect the points to form a straight line.

Additional Considerations

It’s important to note that the line extends infinitely in both directions. Therefore, any point that satisfies the equation y -x 7 will lie on this line.

Summary

In conclusion, graphing the linear equation y - 7 -x involves transforming it into the slope-intercept form, identifying the y-intercept, creating a table of values, and plotting the points on a graph. This process allows us to visualize the linear relationship between x and y.