Lesson 2: Writing Linear Equations in Slope Intercept Form

Why is math used to model real-world situations?

Is one point enough to determine a unique line? Are two points enough? Why or why not?

What does the slope of a linear equation represent in a real-world situation?

Slope
y-intercept
Point
horizontal intercept

F.BF.1 Write a function that describes a relationship between two quantities.

F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

SAT questions related to writing equations: 5-4-11,4-3-8,8-4-7,1-3-12,7-3-19
functions: 8-4-4, 7-4-18, 8-4-18, 2-4-14, 3-4-20, 1-4-5, 7-4-21,
Solving Equations: 5-3-17, 6-4-32, 3-4-7, 8-3-1, 3-3-17, 6-3-17, 1-3-1, 3-3-2, 2-3-1, 7-3-16, 6-3-6

Lesson Description: This lesson focuses on the multi-step process required to determine the equation of a line when the slope is not explicitly given. Students will learn to: Calculate Slope from Two Points: Using the slope formula m = {y_2 - y_1/x_2 - x_1 as the first step in the modeling process. Determine the Y-Intercept (b): Selecting one of the two given points and substituting it, along with the calculated slope, into the y = mx + b template to solve for b. Assemble the Final Function: Consolidating the calculated m and b into the formal function notation f(x) = mx + b. Handle Special Cases: Recognizing when two points result in a horizontal line (same y-values) or a vertical line (same x-values) and writing their unique equations.
Purpose
The purpose of Section 10.2 is to develop analytical independence. In real-world data sets, you are rarely handed the "slope" or the "starting value" on a silver platter. Instead, you might only have two observations (e.g., "In year 2, sales were 40,000, and in year 5, sales were 70,000"). This section empowers students to take those two isolated facts and build a bridge between them, allowing for the interpolation of data between the points and the extrapolation of data into the future.
Depth of Knowledge (DOK) Level
DOK Level 2 & 3
Level 2 (Skill/Concept): Following the three-step procedure: calculate m, solve for b, and write the equation. This requires coordinating multiple algebraic formulas and keeping track of negative signs during subtraction.
Level 3 (Strategic Thinking): Applying this process to real-world scenarios. Students must decide which variable represents the input (x) and which represents the output (y), extract the coordinates from a narrative, and interpret the resulting equation's intercept and slope in the context of the problem.

The 2014 attendance at the Columbus Zoo and Aquarium was about 1.1 million. The zoo's attendance is 2016 was about 13 million. Find the average rate of change for this data, then write an equation that would model the average attendance at the zoo for a given year.

Remind students that x and y in an equation represent any pairs of x- and y-values that satisfy the equation. The coordinates of the given point are one pair of these values. Make sure students understand that while two points can be used to write an equation, real-life prediction equations involve many more data points.

If students are confused by learning more than one way to write a linear equation, then have those students use the definition of slope to derive the slope-intercept form of an equation. This same approach can be used in Lesson 4-3 for the point-slope form of an equation. The logical learner does best when relating new concepts to concepts already learned.

Extension: Write (3, 4) and (5, 4) on the board. Ask students to find b, the y-intercept, for the line through these two points. After they have done this, write (3, 5) and (3, 4) on the board and ask students to find b for the line through these two points and have them explain

Use "you try" pg 236 and practice problems to assess students' understanding of the lesson concepts