Objective
Write linear equations using slope and a given point on the line.
Common Core Standards
Core Standards
The core standards covered in this lesson
8.EE.B.6— Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
Expressions and Equations
8.EE.B.6— Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
8.F.B.4— Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Functions
8.F.B.4— Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Criteria for Success
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Use slope and a point on a line to determine where the line passes through the $$y$$-axis.
- Write a linear equation in the form$$y=mx+b$$ using slope and $$y$$-intercept.
- Write a linear equation for a word problem given rate of change and information representing an ordered pair.
Tips for Teachers
Suggestions for teachers to help them teach this lesson
Lessons 11 and 12 address writing linear equations using information about the line or situation. In Lesson 11, students are given information about the slope or rate of change, as well as information that includes a pair of$$x$$and $$y$$values, in order to determine the $$y$$-intercept or initial value.
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Anchor Problems
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Problem 1
Match each description of a line to the equation that represents it.
| Descriptions | Equations |
| 1. Vertical line through (4, -2) | A.$$y=-2x+4$$ |
| 2. Line with slope of 2 and $$y-$$intercept (0, -4) | B.$$y=-2+4x$$ |
| 3. Line with slope of -2 and $$y-$$intercept (0, 4) | C.$$y=-2$$ |
| 4. Line with slope of -4 and $$y-$$intercept (0, 2) | D.$$x=4$$ |
| 5. Line with slope of 4 and $$y-$$intercept (0, -2) | E.$$y=-4+2x$$ |
| 6. Horizontal line through (4, -2) | F.$$y=-4x+2$$ |
Guiding Questions
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Problem 2
A line passes through the point $$(-5, -3)$$ and has a slope of $$\frac{1}{2}$$.
What is the equation for this line in slope-intercept form?
Guiding Questions
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Problem 3
A taxicab driver charges $2.40 per mile plus a one-time flat fee. A 3-mile ride costs you $10.30.
a.Write a function to represent the cost of a taxicab ride, $$y$$, for $$x$$miles.
b.How much will it cost you to travel 9 miles?
Guiding Questions
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Problem Set
A set of suggested resources or problem types that teachers can turn into a problem set
Fishtank Plus Content
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
Target Task
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Problem 1
Throughout the summer, you save money from your summer job and put it in your savings account. Startingin the fall, you begin withdrawing $35 each week and no longer add any money to the account. After 5 weeks of withdrawing money, you have $514 left in your savings account.
How much money did you start with in your account? What function represents the amount of money in your account, $$y$$, after $$x$$weeks of withdrawals?
Problem 2
Write an equation in slope-intercept form for the line that passes through the point $${(-6, -20)}$$ and has a slope of $$2$$.
Student Response
An example response to the Target Task at the level of detail expected of the students.
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Additional Practice
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
- Include problems where a graph is given with a non-integer y-intercept; students should still be able to find the exact value of the slope from the graph by using the slope and a point on the line.
- EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic C > Lesson 21—Exercises and Problem Set; do not include problems where only two points are given
- Algebra By Example 2.4 Graphing Linear Equations
Lesson 10
Lesson 12
