Graphing Linear Functions Using Given Information

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Objective

SWBAT derive the equation of a line using the slope and the y-intercept.

Big Idea

Students calculate slope and y-intercept before graphing a linear function on a coordinate plane.

Do-Now

10 minutes

When they arrive, students will begin to work on the Do Now. Calculating the rate of change between two points is a topic we have covered, so I will prompt students to refer to their notes if they have difficulty getting started.  

After a few minutes, I will invite six student volunteers will come up to the board to show their work for the do-now. Students can check their work at their seats. 

Next, a volunteer will read the objective: "SWBAT derive the equation of a line using the slope, and the y-intercept". Then, I will ask a student to define the word "derive". Once I am sure that students understand today's objective I will give students a few minutes to discuss what we learned about linear functions and coordinates pairs during our last class.

Guided Notes + Practice

30 minutes

I begin today's presentation by sharing the document Write the Equation of a Line. As a first step, students will graph the equation y = 3x - 5. Next, students pick three points that lie on the line, and, plug the x and y coordinates into the equation.

Instructor's Note: Students completed this same task during our last class, but the focus of it in today's lesson is for students to visualize the importance of "m" and "b" in a linear equation.

After testing three points on the line, I lead the class in a discussion of the prompt "If a point is on a line ......." I will ask students to complete the statement by identifying which parts of the equation Y = 3x - 5 stay the same for every point that they test and which parts can fluctuate. 

After this discussion the students will work at their own pace to complete the worksheet. I plan to bring the class together at select points.

Example One:

Students are asked to find the equation of a line that has a slope of 2, and that passes through the point (4, 7). I will ask students to describe what information we know about the line, and what is still missing. I will then connect our introduction task to what we have been asked to do:

  • We know if a point is on a line when we plug it in to the original equation, a true statement will be formed.
  • We know the point (4, 7) is on the line, so we can simply plug it into the equation.
  • We can use what we know about linear equations to solve for b.
  • If I were to write the equation of a this line, what two elements have to be included? What are the most important parts of this equation? Why?

 

Example Three: 

I will ask the class to describe how this example is different than example one and two, and to list the given information. Students quickly realize that the slope of the line is missing. I will ask the students if they know a way to calculate the slope of the line, and if we have ever calculated the slope of a line between two points in the past. Many of my students realized the deliberateness of our Do-Now from today's class and held it up in the air with excitement.

Students will calculate the equation of the line using the same process from example one and two. After deriving an equation of the line, we will graph the equation to verify that the line indeed passes through the two points.

Independent Practice

30 minutes

Students will complete the Equation of a Line activity independently or in pairs. For each problem, students are given information about a line. They will then use what they have learned to derive the equation of the line in slope intercept form.

On the back of their paper, students will match the equation of each line to the corresponding letter. This letter will be used to fill in the blanks to answer the math riddle.

Closing

10 minutes

I will ask a student to make an analogy between slope intercept form and a puzzle. Students will then complete the Exit Card. The exit cards should be graded directly after class, and the students should then be grouped by the percentage of correct questions for the small group activity to be completed during the next lesson.