Algebra 1 Writing Linear Equations and Functions Worksheet Solutions (PDF)

Algebra 1 math worksheet solutions: Writing Linear Equations and Functions – Maths PDF

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This writing linear answers for Algebra 1 covers writing linear equations and functions (Common Core F-LE.A.2, F-BF.A.1a, A-CED.A.2), with a free PDF to print.

Here are full solutions for the writing linear equations worksheet. Read each step, not just the bold answer, and compare it with your own method. Redo any problem you missed, and note which kind of mistake you made so you can avoid it on the test.

Algebra 1 · Common Core State Standards: F-LE.A.2, F-BF.A.1a, A-CED.A.2

Writing linear answers: exercises 1 to 10

Exercise 1 – Slope and intercept given

Substitute $m = 4$ and $b = -3$ into $y = mx + b$.

$y = 4x – 3$

Exercise 2 – Slope and y-intercept point

The point is on the y-axis, so $b = 5$.

$y = -2x + 5$

Exercise 3 – Equation from a graph

The y-intercept is 1. Slope: $\frac{5 – 1}{2 – 0} = 2$.

$y = 2x + 1$

Exercise 4 – Point and slope

Point-slope: $y – 4 = 3(x – 2)$.

Distribute: $y – 4 = 3x – 6$. Add 4: $y = 3x – 2$.

$y – 4 = 3(x – 2)$; $y = 3x – 2$

Exercise 5 – Fraction slope

Substitute into $y = mx + b$: $1 = -\frac{1}{2}(4) + b$, so $1 = -2 + b$.

$b = 3$.

$y = -\frac{1}{2}x + 3$

Exercise 6 – Two points, positive slope

Slope: $\frac{9 – 5}{4 – 2} = 2$.

Substitute $(2, 5)$: $5 = 2(2) + b$, so $b = 1$.

$y = 2x + 1$

Exercise 7 – Two points

Slope: $\frac{-5 – 7}{4 – (-2)} = \frac{-12}{6} = -2$.

Substitute $(-2, 7)$: $7 = -2(-2) + b$, so $7 = 4 + b$ and $b = 3$.

$y = -2x + 3$

Exercise 8 – Equation from a table

The outputs rise by 3 for each step of 1, so $m = 3$.

Substitute $(1, 7)$: $7 = 3(1) + b$, so $b = 4$.

$y = 3x + 4$

Exercise 9 – Table with steps of 2

As $x$ increases by 2, $y$ decreases by 4, so the slope is $\frac{-4}{2} = -2$.

Substitute $(2, 1)$: $1 = -2(2) + b$, so $b = 5$.

$y = -2x + 5$

Exercise 10 – Parallel line

Parallel lines share the slope 2. Substitute $(3, -1)$: $-1 = 2(3) + b$, so $b = -7$.

$y = 2x – 7$

Exercises 11 and up

Exercise 11 – Perpendicular line

The perpendicular slope is the negative reciprocal of 2, which is $-\frac{1}{2}$.

Substitute $(4, 3)$: $3 = -\frac{1}{2}(4) + b$, so $b = 5$.

$y = -\frac{1}{2}x + 5$

Exercise 12 – Horizontal and vertical

The horizontal line has the constant y-value 2. The vertical line has the constant x-value -3.

$y = 2$ and $x = -3$

Exercise 13 – Standard form

Multiply every term by 4: $4y = 3x – 8$.

Subtract $4y$ from both sides and add 8: $8 = 3x – 4y$.

$3x – 4y = 8$

Exercise 14 – Function notation

The y-intercept is $-4$. Slope: $\frac{5 – (-4)}{3 – 0} = 3$.

$f(x) = 3x – 4$

Exercise 15 – Do three points line up?

Slope of the first pair: $\frac{8 – 2}{3 – 1} = 3$. Second pair: $\frac{14 – 8}{5 – 3} = 3$. The slopes match.

Substitute $(1, 2)$: $b = 2 – 3 = -1$.

Yes; $y = 3x – 1$

Exercise 16 – Cell plan

Cost = fee + rate × texts.

$C(x) = 0.05x + 20$.

$C(300) = 0.05(300) + 20 = 15 + 20 = 35$.

$C(x) = 0.05x + 20$; $35

Exercise 17 – Plumber

The charge rises $60 per hour, so $m = 60$. Then $105 = 60(1) + b$ gives $b = 45$.

$C = 60h + 45$. For 2.5 hours: $60(2.5) + 45 = 195$.

$C = 60h + 45$; $195

Exercise 18 – Candle

Height of the candle.

$H = 12 – 0.75t$.

Solve $12 – 0.75t = 3$: $0.75t = 9$, so $t = 12$. Burn out: $12 – 0.75t = 0$, so $t = 16$.

$H = 12 – 0.75t$; 12 hours; 16 hours

Exercise 19 – Car rental

Rate: $\frac{205 – 135}{5 – 3} = 35$ dollars per day.

Substitute $(3, 135)$: $135 = 35(3) + b$, so $b = 30$.

$C = 35d + 30$. For 7 days: $35(7) + 30 = 275$.

$C = 35d + 30$; $275

Exercise 20 – Filling a pool

Gallons in the pool.

Rate: $\frac{330 – 150}{5 – 2} = 60$ gallons per hour. Substitute: $150 = 60(2) + b$, so $b = 30$.

$G = 60h + 30$. For 8 hours: $60(8) + 30 = 510$.

$G = 60h + 30$; 510 gallons

Exercise 21 – Perpendicular road

The new road (dashed) is perpendicular.

The perpendicular slope is the negative reciprocal of $-\frac{1}{3}$, which is 3.

Substitute $(6, 1)$: $1 = 3(6) + b$, so $b = -17$.

$y = 3x – 17$

Key facts behind this writing linear answers

Key facts

Slope from two points: m = (y₂ – y₁)/(x₂ – x₁).
Find b by substituting a point into y = mx + b.
Point-slope form: y – y₁ = m(x – x₁).
Parallel lines have equal slopes; perpendicular slopes are negative reciprocals.
In a model, the rate is the slope and the starting amount is the y-intercept.

How to use this writing linear answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

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