Task Sets: Graph proportional relationships, interpreting the unit rate as the slope - Common Core Math - Grade 8

Work through problems with immediate feedback

Recall / Warm-Up

Which graph represents a proportional relationship?

A straight line that passes through $(0,0)$

A straight line that crosses the y-axis at $(0,3)$

A curved graph passing through $(0,0)$

Any graph with positive values

For $y = 4x$ , what is the unit rate (and slope)?

A line passes through $(0,0)$ and $(5,15)$ . Find the slope.

Fluency Practice

A table includes $(x,y)$ pairs $(2,5)$ , $(4,10)$ , and $(6,15)$ . What is the unit rate?

Compare $y=2x$ and $y=5x$ .

Which line is steeper?

$y=2x$ is steeper

$y=5x$ is steeper

They are equally steep

Cannot tell without graphing

Which relationship is NOT proportional?

$y=\frac{3}{4}x$

$y=2x+1$

A graph through $(0,0)$ and $(4,8)$

A table where $\frac{y}{x}=6$ for every nonzero $x$

Use points $(2,6)$ and $(7,21)$ on the same line to find slope.

For $y=0.8x$ , when $x$ increases by 1, $y$ increases by ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ , so the slope is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .

unit-rate increase:

slope:

Varied Practice

$Line through origin with slope triangle showing rise 10 and run 4$

The graph passes through $(0,0)$ and $(4,10)$ . Find the slope and unit rate.

$Comparison of rates from a graph and an equation showing 6 is greater than 5$

Relationship A is graphed and passes through $(0,0)$ and $(3,18)$ . Relationship B is given by $d=5t$ .

Find the unit rate for Relationship A.

Which relationship has the greater rate?

Relationship A

Relationship B

They are equal

Cannot determine

Store X table: $(5,4)$ , $(10,8)$ , $(20,16)$ where $(x,y)$ means feet of rope and dollars. Store Y charges $0.90$ dollars per foot. Which store is cheaper per foot?

Store X

Store Y

Same price

Cannot determine

Word Problems

A car's distance-time graph passes through $(0,0)$ and $(8,240)$ where distance is in miles and time is in hours.

What is the car's speed in miles per hour?

Bike A graph passes through $(0,0)$ and $(5,60)$ (miles over hours). Bike B table has $(1,10)$ , $(3,30)$ , $(6,60)$ .

Find Bike A speed.

Which bike is faster, and by how much?

Plan P charges $4$ dollars per notebook. Plan Q has cost equation $C=4n+6$ .

Which statement is true?

Both are proportional with the same unit rate

Only Plan P is proportional

Only Plan Q is proportional

Neither is proportional

Error Analysis

$Comparison of a line through origin and a shifted line that does not pass through origin$

Nia says: "The graph of $y=2x+3$ is a straight line, so it is proportional."

What is Nia's error?

She forgot that proportional graphs must pass through the origin

She should have multiplied x by 3

She should have used a curved graph

Her claim is correct

Omar uses points $(1,4)$ and $(4,10)$ on a line.
He computes slope as $\frac{10}{1}=10$ and says,
"If I choose different points, slope changes anyway."

Which feedback is best?

Correct slope is $\frac{10-4}{4-1}=2$ ; slope uses changes and is constant on a line

Slope should be $\frac{4}{10}$ because x is always numerator

You should use only points that include the origin

Slope cannot be found from points

Challenge / Extension

Three plans are represented differently: Plan A equation $C=0.08t$ , Plan B graph through $(0,0)$ and $(100,9)$ , Plan C table $(50,3.5)$ and $(200,14)$ .

What is each plan's cost per text (A, B, C in dollars per text)?

Rank plans from cheapest to most expensive per text and justify.