Chapter 1, Lesson 8

In this lesson students will:

• calculate the and intercepts of a linear equation
• use the intercepts of a linear equation to sketch the linear equation
• interpret the solution of a system of linear equations as the point of intersection of two lines

Systems of Linear Equations

Intercepts of a system of Linear Equations

In this lesson the main goal will be to sketch a system of linear equations in the Cartesian plane (-plane). There are several methods to do this, but perhaps the simplest one is to find the and intercepts of each linear equation. An intercept is where our line will cross the -axis or -axis. If our line crosses the -axis, we call this point on the line the intercept. If our line crosses the -axis, we call this point on the line the intercept.

To find and sketch an -intercept:

1. Substitute into the linear equation.
2. Solve for .
3. For the value that you found in part 2, count that many spaces along the -axis and draw a point.

To find and sketch a -intercept:

1. Substitute into the linear equation.
2. Solve for .
3. For the value that you obtained in part 2, count that many steps along the -axis and draw a point.

If you connect the and intercepts of a given linear equation with a ruler this will give you a rough sketch of the line it represents in the Cartesian plane. The following video will go through an example of how this is done.

Interpreting the Point of Intersection

Once you have drawn a rough sketch of your linear system, you might notice that the two lines intersect at a specific point. It turns out that the solution to the linear system that we found algebraically in chapter BM1.7 has a geometric representation as this intersection point. This is a nice way to double-check that the solution we obtained by solving algebraically seems reasonable given our drawing of the two lines. The short video below will connect these two ideas together for you.