Algebra 1 Graphing Linear Equations Worksheet (PDF)

Algebra 1 math worksheet: Graphing Linear Equations – Maths PDF

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This graphing linear worksheet for Algebra 1 covers graphing linear equations (Common Core A-REI.D.10, F-IF.C.7a, A-CED.A.2), with a free PDF to print.

Graphing linear worksheet (Algebra 1) – first page of the printable PDF

These 20 problems practice graphing linear equations (Common Core A-REI.D.10, F-IF.C.7a, and A-CED.A.2). You will graph lines from slope-intercept, standard, and point-slope forms, find intercepts, test points, and model situations with linear equations. The first problems are short skill checks, and the last six are word problems that need several steps. Work in order and show every line of your work, because a bare answer earns little credit on a test.

Algebra 1 · Common Core State Standards: A-REI.D.10, F-IF.C.7a, A-CED.A.2

Graphing linear worksheet: exercises 1 to 10

Exercise 1 – Slope and intercept

Identify the slope and the y-intercept of $y = 3x – 5$.

Exercise 2 – Fraction slope

Identify the slope and the y-intercept of $y = -\frac{3}{4}x + 5$.

Exercise 3 – Graph y = 2x + 1

Graph $y = 2x + 1$.

Exercise 4 – Negative slope

Graph $y = -3x + 2$.

Exercise 5 – Fraction slope graph

Graph $y = \frac{3}{2}x – 2$.

Exercise 6 – Intercepts

The line $3x + 4y = 12$.

Find the x-intercept and y-intercept of $3x + 4y = 12$.

Exercise 7 – Graph with intercepts

Graph $2x – y = 4$ using its intercepts.

Exercise 8 – Standard to slope-intercept

Rewrite $6x + 3y = 9$ in slope-intercept form.

Exercise 9 – Horizontal and vertical

Graph the lines $y = -2$ and $x = 3$.

Exercise 10 – Point-slope form

Write an equation in point-slope form for the line with slope 2 through $(3, 1)$, then rewrite it in slope-intercept form.

Exercises 11 and up

Exercise 11 – Graph point-slope

Graph $y + 2 = \frac{1}{2}(x – 4)$.

Exercise 12 – Is the point on the line?

Decide whether each point is on the line $y = 2x + 1$: (a) $(3, 7)$ (b) $(-1, 4)$.

Exercise 13 – Match the graph

Cost of a trampoline park.

The graph shows the cost $y$ in dollars of $x$ hours at a trampoline park. Write an equation for the cost and say what the slope means.

Exercise 14 – Complete a table

Solutions of the equation.

Complete a table of three solutions of $y = -x + 5$ using $x = -2$, $x = 0$, $x = 3$.

Exercise 15 – Compare steepness

Line A is $y = 3x + 1$. Line B passes through $(0, 4)$ and $(2, 12)$. Which line is steeper?

Exercise 16 – Bike rental

Ethan rents a bike for an $8 fee plus $6 per hour. The cost is $y = 6x + 8$. Identify the slope and intercept in context, then find the cost for 3.5 hours.

Exercise 17 – Fundraiser tickets

At a Little League fundraiser, adult tickets cost $5 ($x$) and student tickets cost $2 ($y$). The goal is $40, so $5x + 2y = 40$. Find the intercepts and explain them. Then find $y$ when $x = 4$.

Exercise 18 – Draining tank

Tank readings.

A tank holds 60 gallons and drains at 3 gallons per minute, so $y = 60 – 3x$ gallons remain after $x$ minutes. Find both intercepts, explain them, and give a reasonable domain.

Exercise 19 – Moving company

A moving company charges $y = 25x + 50$ dollars for $x$ hours. Find the cost of 4 hours and the number of hours for $225.

Exercise 20 – Temperature graph

The formula $F = \frac{9}{5}C + 32$ converts Celsius to Fahrenheit. Identify the slope and intercept and find $F$ when $C = 100$.

Exercise 21 – Equation from two points

A line.

Write the equation of the line through $(-2, 4)$ and $(4, -2)$.

View solution

Key facts behind this graphing linear worksheet

Key facts

Every point on the line is a solution of the equation, and every solution is on the line.
In y = mx + b, m is the slope and b is the y-intercept.
Find intercepts by setting x = 0 for the y-intercept and y = 0 for the x-intercept.
Point-slope form y – y₁ = m(x – x₁) uses a known point and the slope.
y = k is horizontal with slope 0; x = h is vertical with undefined slope.

How to use this graphing linear 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 graphing linear worksheet as a PDF with the button below and keep it with your notes.

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Algebra 1 Graphing Linear Equations Worksheet (PDF)

Graphing linear worksheet: exercises 1 to 10

Exercises 11 and up

Key facts behind this graphing linear worksheet

How to use this graphing linear worksheet

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