Taxi Company A charges a fixed fee of $\text{€}4.00$ plus $\text{€}1.50$ per kilometre travelled. Taxi Company B charges a fixed fee of $\text{€}2.50$ plus $\text{€}2.00$ per kilometre travelled. Defining suitable variables, write down the linear equations for the cost of travelling with Company A and Company B. Use your graphic display calculator to determine the distance for which both taxi companies cost exactly the same amount.

Let $C$ be cost and $d$ be distance in km. Company A: $C_A = 1.50d + 4.00$ . A1 Company B: $C_B = 2.00d + 2.50$ . A1 Set $1.50d + 4.00 = 2.00d + 2.50$ . (M1) CG50: MENU 5 (Graph) . Y1 = 1.5x + 4 , Y2 = 2x + 2.5 . DRAW and press G-Solv -> F5 (ISCT) . (M1) Intersection at $x = 3$ . Distance is $3 \text{ km}$ . A1

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IB Maths AA SL · Unit 2: Functions

IB Maths AA SL Equations of Straight Lines Questions

Updated October 2026

Exam-style IB Maths AA SL equations of straight lines questions with worked solutions. Start with the 3 fully worked examples below — each is solved step by step, showing the working that earns the marks — then try the practice questions and check your working against the mark scheme.

30 questions
Paper 1: 23
Paper 2: 7
9 easy
12 medium
5 hard
4 very hard
3 worked examples

Practise Equations of Straight Lines questions →

What's examined in AA SL equations of straight lines

The question bank covers these equations of straight lines question types (number of questions in brackets):

Line equations and properties (13)
Parallel and perpendicular lines (11)
Midpoints and intersections (6)

Key formulas

Equation of a straight line: $y - y_{1} = m (x - x_{1})$
Gradient: $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

In the same notation as the IB formula booklet. All AA SL formulas →

Explained, with a worked example: Equation of a straight line · Gradient formula · Midpoint formula

Equations of Straight Lines worked examples

Worked example 1: Finding gradients and intercepts · easy

The equation of a line $L_{1}$ is given by $3 x + 4 y - 12 = 0$ . Find the exact gradient of $L_{1}$ and the coordinates of its $x$ and $y$ -intercepts.

Solution

5 steps · 1 to fill in

Examiner tip: Always remember to divide every single term by the coefficient of

y

when rearranging into

y = m x + c

. Forgetting to divide the constant term is a frequent careless error that ruins the

y

-intercept.

Worked example 2: Perpendicular bisectors · medium

Find the equation of the perpendicular bisector of the line segment joining the points $A (- 2, 5)$ and $B (4, - 7)$ . Give your answer in the form $a x + b y + d = 0$ , where $a, b, d \in Z$ .

Solution

5 steps · 1 to fill in

Examiner tip: Students frequently forget to use the midpoint for the perpendicular bisector, mistakenly substituting one of the original endpoints (

A

B

) into the line equation instead.

Worked example 3: Intersection and perpendicular lines · hard

Line $L_{1}$ has the equation $5 y - 2 x + 1 = 0$ . Point $A$ lies on $L_{1}$ and has a $y$ -coordinate of $3$ . A second line $L_{2}$ is perpendicular to $L_{1}$ and passes through $A$ . Find the equation of $L_{2}$ in the form $y = m x + c$ .

Solution

5 steps · 1 to fill in

Examiner tip: When finding the perpendicular gradient, remember to both flip the fraction and change the sign (the negative reciprocal). Doing only one of these steps is a classic Paper 1 trap.

Try these IB Maths AA SL equations of straight lines questions

Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area. One of them has its full worked solution here, open to everyone.

Question 1 · easy · 3 marks · Paper 1

The coordinates of point $A$ are $(1, 3)$ and the coordinates of point $B$ are $(4, 9)$ . Find the equation of the line passing through $A$ and $B$ . Give your answer in the form $y = m x + c$ .

Attempt it and see the mark scheme →

Question 2 · medium · 5 marks · Paper 2

Taxi Company A charges a fixed fee of $€ 4.00$ plus $€ 1.50$ per kilometre travelled. Taxi Company B charges a fixed fee of $€ 2.50$ plus $€ 2.00$ per kilometre travelled.

Defining suitable variables, write down the linear equations for the cost of travelling with Company A and Company B.
Use your graphic display calculator to determine the distance for which both taxi companies cost exactly the same amount.

Full worked solution Free, no sign-in

Let $C$ be cost and $d$ be distance in km.
Company A: $C_{A} = 1.50 d + 4.00$ . A1
Company B: $C_{B} = 2.00 d + 2.50$ . A1
Set $1.50 d + 4.00 = 2.00 d + 2.50$ . (M1)
CG50: MENU 5 (Graph). Y1 = 1.5x + 4, Y2 = 2x + 2.5.
DRAW and press G-Solv -> F5 (ISCT). (M1)
Intersection at $x = 3$ .
Distance is $3 km$ . A1

Every question here has a full worked solution. See them all →

Question 3 · hard · 4 marks · Paper 1

The line passing through the points $A (k, 4)$ and $B (6, k)$ has a gradient of $3$ . Find the exact value of $k$ .

Attempt it and see the mark scheme →

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FAQ

How many IB Maths AA SL equations of straight lines questions are there?

There are 30 exam-style equations of straight lines questions in the AA SL question bank (Paper 1: 23 · Paper 2: 7), graded 9 easy, 12 medium, 5 hard, 4 very hard. Every question has a full IB-style mark scheme (M, A and R marks).

Is equations of straight lines on Paper 1 or Paper 2?

Both. In the bank, Paper 1: 23 · Paper 2: 7. Paper 1 is non-calculator, so practise the exact-value algebra as well as the GDC methods.

Where can I get the mark schemes?

Open the AA SL Unit 2 practice page: every question has a step-by-step IB-style mark scheme, and you can photograph your working for instant AI marking. The worked examples on this page are free.

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Save your answers and track your progressA free account remembers the questions you have done on every topic and brings you back to this page.

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Free ready-to-teach lessons (slides and teacher notes): Gradient & intercepts of a line · Parallel & perpendicular lines.

IB Maths AA SL Equations of Straight Lines Questions

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What's examined in AA SL equations of straight lines

Key formulas

Equations of Straight Lines worked examples

Worked example 1: Finding gradients and intercepts · easy

Solution

Worked example 2: Perpendicular bisectors · medium

Solution

Worked example 3: Intersection and perpendicular lines · hard

Solution

Try these IB Maths AA SL equations of straight lines questions

Question 1 · easy · 3 marks · Paper 1

Question 2 · medium · 5 marks · Paper 2

Full worked solution Free, no sign-in

Question 3 · hard · 4 marks · Paper 1

Revise equations of straight lines for the exam

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