Curriculum / Math / 8th Grade / Unit 5: Linear Relationships / Lesson 12
Math
Unit 5
8th Grade
Lesson 12 of 15
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Write linear equations using two given points 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 12, students are given two points on the line or two solutions to a situation in order to determine the slope or rate of change and 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
A line is shown in the coordinate plane below.
What is the equation for the line shown?
A line passes through the points (4, 3) and (9, -7).
What is the equation for this line in slope-intercept form?
A model airplane reaches a maximum altitude and then begins to descend at a constant rate in feet per second. After falling for 12 seconds, the model airplane has an altitude of 212 feet. After falling for 25 seconds, the model airplane’s altitude is 95 feet.
What function represents the altitude of the model airplane, $$y$$, after $$x$$ seconds of falling?
A set of suggested resources or problem types that teachers can turn into a problem set
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
Tickets to a concert are available for early access on a special website. The website charges a fixed fee for early access to the tickets, and the tickets to the concert all cost the same amount with no additional tax. A friend of yours purchases 4 tickets on the website for a total of $162. Another friend purchases 7 tickets on the website for $270.
What function represents the total cost, $$y$$, for the purchase of $$x$$ tickets on the website?
Write an equation in slope-intercept form for the line that passes through the points $${(-2, -3)}$$ and $${(1, 12)}$$.
An example response to the Target Task at the level of detail expected of the students.
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 11
Lesson 13
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 slope and a given point 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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