Curriculum / Math / 8th Grade / Unit 5: Linear Relationships / Lesson 7
Math
Unit 5
8th Grade
Lesson 7 of 15
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Determine slope from coordinate points. Find slope of horizontal and vertical lines.
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 foundational standards covered in this lesson
7.NS.A.1 — Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
7.NS.A.2.B — Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
In determining slope from coordinate points, students will need a strong grasp of adding and subtracting signed numbers (standard 7.NS.1). If needed, review these concepts and skills prior to this lesson.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
The table below shows some solution values for the equation $${{y=-3x+2}}$$.
Use the values in the table to determine the slope of the line represented by $${{y=-3x+2}}$$.
A line passes through the points $$(-1, 3)$$ and $$(5, 11)$$.
a. Find the slope of the line.
b. Is the point $$(-4, -1)$$ on the same line as the other two points? Use slope to justify your answer.
Find the slope of line $$m$$ and line $$n$$, shown below.
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
Samantha found the slope of the line that passed through the points $${(2, 6)}$$ and $${(-4, 8)}$$. Her work is shown below.
$${{8-6\over {2-(-4)}} = {2\over 2+4 }= {2\over 6} = {1\over3}}$$
Samantha made an error in her work. Describe the error and then find the correct slope of the line through the two given points.
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 6
Lesson 8
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
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 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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