Algebra 1 Writing Linear Equations and Functions Test with Point Values (PDF)

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

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This writing linear test 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.

Take this 20-point, 45-minute test to measure your skill with writing linear equations and functions (F-LE.A.2, F-BF.A.1a, and A-CED.A.2). Read each question carefully, show your work, and check units and signs before you move on. If you get stuck, skip the question and return to it at the end.

Time and points

About this test

Grade: Algebra 1
Chapter: Writing Linear Equations and Functions
Standards: F-LE.A.2, F-BF.A.1a, A-CED.A.2
Time: 45 minutes
Total: 20 points

Writing linear test: questions

Question 1 – Slope-intercept form [2 pts]

Write an equation in slope-intercept form.

Slope 5, y-intercept \(-1\). (1 point)
Slope \(-\frac{1}{3}\), passes through \((0, 4)\). (1 point)

Question 2 – Point-slope [2 pts]

A line has slope 4 and passes through \((-1, 6)\). Write its equation in point-slope form and slope-intercept form.

Question 3 – Two points [2 pts]

Write the equation of the line through \((2, -3)\) and \((6, 5)\).

Question 4 – Equation from a graph [2 pts]

Graph for question 4.

Write the equation of the line shown.

Question 5 – Equation from a table [2 pts]

Table for question 5.

The table shows a linear function. Write its equation.

Question 6 – Parallel line [2 pts]

Write the equation of the line through \((2, 5)\) that is parallel to \(y = -3x + 1\).

Question 7 – Perpendicular line [3 pts]

A line is perpendicular to \(y = 3x – 4\) and passes through \((6, 2)\).

State its slope. (1 point)
Write its equation in slope-intercept form. (2 points)

Question 8 – Taxi fare model [3 pts]

Two taxi rides.

A taxi fare is linear in the miles driven. Two fares are shown in the table.

Find the cost per mile. (1 point)
Write an equation for the fare \(C\) for \(m\) miles. (1 point)
Find the fare for 15 miles. (1 point)

Question 9 – Standard form [2 pts]

Write \(y = -\frac{3}{5}x + 4\) in standard form with integer coefficients.

Key facts behind this writing linear test

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 test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Algebra 1 chapters: Algebra 1 math.

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