Algebra 1 Slope and Rate of Change Worksheet (PDF)

Algebra 1 math worksheet: Slope and Rate of Change – Maths PDF

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This slope rate of change worksheet for Algebra 1 covers slope and rate of change (Common Core F-IF.B.4, F-IF.B.6, F-LE.A.1b), with a free PDF to print.

Slope rate of change worksheet (Algebra 1) – first page of the printable PDF

Use these 20 problems to master slope and rate of change (Common Core F-IF.B.6, F-IF.B.4, and F-LE.A.1b). You will find slope from points, graphs, and tables, interpret rates in context, and compute the average rate of change of a function over an interval. They move from quick warm-ups to multistep word problems, so slow down on the last six and check that each answer makes sense.

Algebra 1 · Common Core State Standards: F-IF.B.4, F-IF.B.6, F-LE.A.1b

Slope rate of change worksheet: exercises 1 to 10

Exercise 1 – Positive slope

Find the slope of the line through $(2, 5)$ and $(5, 17)$.

Exercise 2 – Negative slope

Find the slope of the line through $(-2, 5)$ and $(3, -5)$.

Exercise 3 – Zero slope

Find the slope of the line through $(3, 4)$ and $(7, 4)$.

Exercise 4 – Vertical line

Find the slope of the line through $(2, 1)$ and $(2, 6)$.

Exercise 5 – Slope from a graph

A line on the coordinate plane.

Find the slope of the line.

Exercise 6 – Slope from a table

A table of a linear function.

Find the slope of the linear function shown in the table.

Exercise 7 – Classify the slope

Without a graph, decide whether each line through the given points has positive, negative, zero, or undefined slope: (a) $(1, 3), (5, 3)$ (b) $(2, 7), (2, -1)$ (c) $(0, 4), (3, 1)$ (d) $(-2, -1), (4, 5)$.

Exercise 8 – Ramp

A wheelchair ramp rises 2 feet over a horizontal distance of 24 feet. Find its slope.

Exercise 9 – Missing coordinate

The line through $(2, 3)$ and $(6, y)$ has slope 2. Find $y$.

Exercise 10 – Is it linear?

A table.

Decide whether the table represents a linear function. Explain with rates of change.

Exercises 11 and up

Exercise 11 – Fraction coordinates

Find the slope of the line through $\left(-\frac{1}{2}, 1\right)$ and $\left(\frac{3}{2}, 5\right)$.

Exercise 12 – Savings rate

Jamal had $50 after week 2 and $95 after week 5. Assuming a constant rate, find his savings rate in dollars per week.

Exercise 13 – Road trip graph

Distance on a road trip.

The graph shows the distance of a car from home. Find the slope and explain what it means.

Exercise 14 – Meaning of the intercept

A trampoline park charges $y = 15 + 8x$ dollars for $x$ hours. Explain the slope and the y-intercept in this context.

Exercise 15 – Average rate of change

A skateboard ramp’s height in inches is modeled by $h(x) = 2x^{2} – x$, where $x$ is the horizontal distance in feet. Find the average rate of change of the height from $x = 2$ to $x = 5$.

Exercise 16 – Falling temperature

At 2 p.m. the temperature was 68°F. At 6 p.m. it was 44°F. Find the average rate of change and interpret it.

Exercise 17 – Plant growth

Height of a bean plant.

A bean plant’s height is recorded in the table. Find the rate of change and write what it means.

Exercise 18 – Compare speeds

Car A drives 150 miles in 3 hours. Car B drives 220 miles in 5 hours. Find each average speed and tell which car is faster.

Exercise 19 – Hiker's trip

A hiker’s distance from home.

The graph shows a hiker’s distance from home. Find the rate of change on each interval: 0 to 1 hour, 1 to 2 hours, and 2 to 3 hours. Describe what the hiker is doing.

Exercise 20 – Projectile

A ball’s height in feet is $h(t) = -16t^{2} + 64t$. Find the average rate of change from $t = 0$ to $t = 2$ and from $t = 1$ to $t = 3$. Explain the second answer.

Exercise 21 – Not constant growth

A table of values.

Find the rates of change between consecutive rows. Is the rate constant? What happens to the rate?

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Key facts behind this slope rate of change worksheet

Key facts

Slope = rise ÷ run = (y₂ – y₁)/(x₂ – x₁).
Positive slope rises, negative slope falls, horizontal lines have slope 0, vertical lines are undefined.
In a context, slope is a rate of change with units like dollars per hour.
A linear function has the same rate of change between any two points.
Average rate of change over [a, b] is (f(b) – f(a))/(b – a).

How to use this slope rate of change worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the slope rate of change worksheet as a PDF with the button below and keep it with your notes.

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Algebra 1 Slope and Rate of Change Worksheet (PDF)

Slope rate of change worksheet: exercises 1 to 10

Exercises 11 and up

Key facts behind this slope rate of change worksheet

How to use this slope rate of change worksheet

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