Curriculum / Math / 8th Grade / Unit 5: Linear Relationships / Lesson 11
Math
Unit 5
8th Grade
Lesson 11 of 15
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Write linear equations using slope and a given point on the line.
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.
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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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.Â
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Match each description of a line to the equation that represents it.
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?
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?
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Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Throughout the summer, you save money from your summer job and put it in your savings account. Starting in 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?
Write an equation in slope-intercept form for the line that passes through the point $${(-6, -20)}$$ and has a slope of $$2$$.
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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.
Lesson 10
Lesson 12
Topic A: Comparing Proportional Relationships
Review representations of proportional relationships.
8.EE.B.5
Graph proportional relationships and interpret slope as the unit rate.
Compare proportional relationships represented as graphs.
Compare proportional relationships represented in different ways.
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Topic B: Slope and Graphing Linear Equations
Graph a linear equation using a table of values.
8.F.B.4
Define slope and determine slope from graphs.
8.EE.B.6
Determine slope from coordinate points. Find slope of horizontal and vertical lines.
8.EE.B.6 8.F.B.4
Graph linear equations using slope-intercept form $${y = mx + b}$$.
8.EE.B.6 8.F.A.3
Write equations into slope-intercept form in order to graph. Graph vertical and horizontal lines.
Topic C: Writing Linear Equations
Write linear equations from graphs in the coordinate plane.
Write linear equations using two given points on the line.
Write linear equations for parallel and perpendicular lines.
Compare linear functions represented in different ways.
8.F.A.2 8.F.B.4
Model real-world situations with linear relationships.
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