Graphing Linear Functions in Standard Form (Day 1 of 2)

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Objective

SWBAT graph a linear function in standard form by calculating the intercepts. SWBAT create an equation of a line in standard form by analyzing a real world scenario.

Big Idea

Students will analyze the importance of intercepts in linear function, and use them to graph lines that are in an unfamiliar format.

Do-Now

10 minutes

Students will complete the Investigate intercepts Do Now at the beginning of class. Before completing this assignment, students should already be able to identify the x and y intercepts of line on a graph. 

After 4 minutes we will review the Do-Now as a whole group. I will class on multiple students to elaborate their answers, especially with number 3 and 6. Eventually the students will come to the realization that the x intercept will always be of the form (#,0) and the y-intercept will always be in the form (0, #) because of the coordinates lie on an axis.

I will challenge the class to validate their claim by sketching two lines on their Do-Now to see if the the x and y intercept will ever not contain a "0".

Next, a volunteer will read the objective "SWBAT graph lines in standard form by finding the intercepts". I will ask the students to make a predication about how we can use the coordinates of intercepts to graph a line.

Guided Notes + Practice

30 minutes

Students will transition into the lesson using the Standard Form presentation.

Slide 3: Students will spend two minutes discussing the Turn and Talk problem with a partner. This task is familiar to students, as they practiced this skill in-depth during the Linear Functions unit. The students will then share their answers aloud. I will ask students to identify the variable in the equation, and to share what purpose it serves.

The purpose of this example is for students to make a connection between the role of 

Slide 4: Next, I will invite the class to construct another equation to fit Example One. Many students will mistakenly create the equation "4x + 2x = 20". I will ask students to analyze the correctness of this equation given that 4x + 2x = 20 is the same thing as 6x = 20. If 6x = 20, then it is implied that it takes 6 hours to finish a book or magazine. 

I will refer back to the Turn and Talk example, by asking students to compare and contrast the two problems. Example one has to have two different variables because Kashanae is reading both books and magazines. In the Turn and Talk problem, she was only reading books.

Students will discover that two variables are needed in order to answer this question, because we cannot use the same variable to represent two items with different rates of change.

Slide 5: Students will take notes on the Standard Form of a linear equation using their Guided Notes. 

Even though Standard Form is generally accepted as ax + by = c; a ≥ 0, I have deliberately chosen not to stress this with my students. It is in my personal opinion that this rule is taught as a tradition, but is not justifiable time spent in the classroom because a "negative a" will not change the outcome of the graph of the line, or affect the validity of the solution at all.

Slide 7: Using our sample equation, 4x + 2y = 20, I will show students that we can use our knowledge of intercepts to graph a line that is in standard form:

  • We know that when a line crosses the x axis its y-value is always zero. If we substitute a 0 into the y in the equation 4x + 2y = 20, we will know where the x-intercept is. 4x + 2(0) = 20.
  • We know that when a line crosses the y axis its x-value is always zero. If we substitute a 0 into the x in the equation 4x + 2y = 20, we will know where the x-intercept is. 4(0) + 2y = 20.
  • The line crosses the graph at (5, 0) and (0, 10). The other points on the graph correspond to the amount of reading Kashanae can complete during her trip. 
    • 5 books, 0 magazines
    • 4 books, 2 magazines
    • 3 books, 4 magazines
    • 2 books, 6 magazines
    • 1 book,  8 magazines
    • 0 books, 10 magazines

 

Independent Practice

30 minutes

Students will practice graphing lines using intercepts using the this assignment and with the ETA Hand to Mind product VersaTiles. Students will match correct responses to the numbered tiles in the black VersaTile case. If you do not have a VersaTiles classroom set, the assignment can still be completed by having students match questions and responses with pencil and paper.

Closing

10 minutes

I will ask two students to give a summary of what we learned in class today. I will ask a third student to describe how the Standard Form of a line is useful in Algebra. Students will then complete an Exit Card.