Lesson plan

In this lesson, students will apply their previous knowledge to represent a real-world linear relationship. The best way to introduce graphing a line using slope-intercept form for `8`th graders is allowing students to use what they notice about a graph. Students will then practice graphing lines using slope-intercept form. You can expect this lesson to take one `45`-minute class period.

Grade 8

Linear Relationships And Functions

8.F.B.4

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Students will be able to graph a line using slope-intercept form.

- Teacher slideshow
- Blank coordinate planes printout
- Online Practice

To teach graphing a line using slope-intercept form, start the lesson by giving students a real-world linear example and having them represent it as a table, graph, or both. The goal is to activate students’ prior knowledge and gauge what they already understand about linear relationships. Allow students the opportunity to discuss their strategies.

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There are several questions you can pose to students to further discussion:

(`1`) How do you decide what `x` and `y` represent in context?

(`2`) How are the graph and table of values related?

(`3`) Is there a pattern to the table or graph? If so, explain.

(`4`) Are all values of `x` reasonable for this situation?

From the discussion, students should have recognized that it was a linear relationship, which has a constant rate of change. Highlight the `y`-intercept and slope for the graph of the problem, then explain that there is a commonly used formula to represent linear relationships called slope-intercept form.

Because of the significance of this formula, you may consider telling students that it will continue to be used in high school and beyond. Review the ideas of slope (or rate of change) and `y`-intercept. Highlight the fact that the sign for the `y`-intercept is based off of whether there is addition or subtraction.

Go through the next several guided examples with students. If you haven’t already given your students coordinate planes to help them make their graphs, you may want to use the __printable blank coordinate planes sheet__.

With each example, guide students through the following:

- Identify the slope and `y`-intercept of the equation.
- Plot the `y`-intercept.
- Determine the direction the line should be drawn based on whether the slope is positive or negative.
- Count the slope using rise over run starting at the `y`-intercept.
- Connect the points and extend the line!

Allow students the opportunity to come to the board to show the class how they graphed the line.

It is important to keep an eye out for the following misconceptions that students may have:

- The direction of the line is opposite of the sign of the slope
- If students are plotting slope as a negative when it should be positive, remind them that “up” and “right” from the `y`-intercept are positive directions.

- The slope plotted is run over rise instead of rise over run.
- If students are using the reciprocal to plot slope, remind them that it is always “rise over run”.

- The slope plotted from the origin instead of the `y`-intercept
- The `y`-intercept plotted has the opposite sign of the formula
- The `y`-intercept is plotted on the `x`-axis.

For this activity, students should graph four different lines with slope-intercept form. Students can use the __printable blank coordinate planes sheet__ so that each line is graphed on its own. You can encourage students to work together, check each other’s work, and justify their reasoning.

After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn lets you access tons of practice problems for graphing a line using slope-intercept form. Check out the online practice and assign to your students for classwork and/or homework!

Graphing a Line Using Slope-Intercept Form Practice

Problem 1 of 5

<p>Graph the line of the equation:</p> <p>`y = -3/2 x + 5`</p><selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><LineGraph data-props='{ "options": { "x_min": -10, "y_min": -10, "y_max": 10, "x_max": 10, "cell_size": 15, "x_interval": 1, "y_interval": 1 }, "points": [], "line_segments": [] }'></LineGraph ></selectivedisplay>

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