June 10, 2009

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This lesson focuses on using x- and y-intercepts to quickly graph equations. It also covers how to find intercepts Algebraically without reference to the graph.

- Mathematics > General
- Mathematics > Algebra
- Mathematics > Equations
- Mathematics > Graphing
- Mathematics > Problem Solving

- Grade 6
- Grade 7
- Grade 8
- Grade 9
- Grade 10

Curriki Rating

On a scale of 0 to 3

3On a scale of 0 to 3

This resource was reviewed using the Curriki Review rubric and received an overall Curriki Review System rating of 3, as of 2009-07-08.

Content Accuracy: 3

Appropriate Pedagogy: 3

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**Learning Objectives:**

1. Students will acquire the concept of x- and y-intercepts.

2. Students will find intercepts of a 2-variable equation Algebraically.

3. Students will use intercepts to quickly graph a 2-variable linear equation.

**Materials:**

Graph paper/whiteboards

Colored pencils/dry erase markers

Rulers

**Procedures:**

Remind students what they learned during the last class: 2-variable equations can be graphed as a straight line. Have them work in groups to graph the following equation:

*3x + 4y = 12*

Have groups report back to the class by showing the line they have drawn and explaining the ordered pairs they used to draw it. Ask students if any ordered pairs were particularly easy to find (try to lead discussion to draw out the concept that intercepts are the easiest ordered pairs to identify).

Define x- and y-intercepts for the class and show them briefly how to quickly find them using Algebra (i.e. plugging *0* in for one of the variables to get the opposite intercept). Place particular emphasis that in order to find the *x-*intercept, you must plug 0 in for ** y**. (This is often confusing for beginning students.)

Remind students that it only really requires two points to determine a straight line. Therefore, if you are able to find the two intercepts, you can quickly draw the graph of an equation. Ask them if they can think of drawbacks to this method, or times when it would be impracticable (try to elicit that any non-integer intercept will inherently be inaccurate when graphed). So, this method has its limitations, but it can definitely speed things up!

Now, refer to the following situation for the next example:

*The Algebra class is selling popcorn for its fundraiser. The popcorn company charges a $24 enrollment fee and $3 per bag of popcorn. If the class charges over $3 per bag, then the rest of the money is their profit. Determine the equation for the cost curve for this situation, find the two intercepts, and graph the cost curve.*

Have the class work with their groups to solve this problem. In the process, make sure that the students are able to identify and understand that the y-intercept is in fact the fixed cost of the business.

Now, use the following example:

*Johnny Robot runs at an incredible 15 m/sec. If Johnny starts 15 m beyond the starting gun when he hears it and begins running at full speed, write an equation where y represents the distance he has run and x represents the number of minutes he has been running.*

Have student pairs work to identify intercepts and graph this situation. Also, have them identify which part of the situation is the y-intercept.

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