Back to Tutor Intake Assessment: Graph proportional relationships, interpreting the unit rate as the slope

8.EE.B.5 Tutor Intake -- Proportional Graphs and Slope

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Grade 8·8 problems·~8 min·Common Core Math - Grade 8·container·8-ee-b-5

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Concepts

A graph shows a straight line that crosses the y-axis at
$(0, 3)$ instead of at the origin. Is this relationship
proportional?

No — a proportional relationship's graph must be a straight line AND pass through the origin; this line misses the origin.

Yes — any straight-line graph represents a proportional relationship.

Yes, as long as the line has a positive slope.

No — proportional relationships can never be represented by a straight line.

A proportional relationship has equation $y = 4x$ . What is the
relationship between its unit rate and the slope of its graph?

They are the same number — both equal 4.

They are different quantities that happen to use the same equation but measure different things.

The unit rate is 4, but the slope must be computed separately using the slope formula and could be a different value.

The slope is always exactly double the unit rate.

Procedures

A relationship is proportional with equation $y = 5x$ . What is
the value of $y$ when $x = 0$ ? (This is the point where the
graph crosses the origin.)

A proportional relationship has unit rate 7 (that is, $y = 7x$ ).
What is the slope of its graph?

A line passes through the points $(2, 6)$ and $(4, 12)$ . Compute
the slope using rise over run.

The same line from the previous problem also passes through
$(1, 3)$ and $(5, 15)$ . Compute the slope using this different
pair of points.

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