Lesson 1: 4-1 Writing Equations in Slope-Intercept Form
Duration of Days: 5
Lesson Objective
Write an equation of a line in slope-intercept form given the slope and one point.
Write an equation of a line in slope-intercept form given two points.
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?
linear extrapolation
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,
Write an equation in slope-intercept form given different types of information. If the slope of a line and a point on the line are given, substitute the values of m, x, and y into the equation for slope-intercept form and solve for b. If given two points on a line, find the slope of the line and then pick one point and substitute the values of m, x, and y into the equation for slope-intercept form and solve for b.
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
Exercises 1-9
Exercises 53-58
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