Graphing Linear Equations

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Graphing Linear Equations — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionParallel and Perpendicular Lines IntroductoryConcept Practice

2 marks~3 minCriterion A

A city planner is designing a rectangular street grid. On a map, one main street passes through points

A(1, 2)

and

B(5, 10)

Calculate the slope of the main street. [1]

A proposed avenue has equation

y = 2x + 3

. Justify whether this avenue should be approved as a street running parallel to the main street. [1]

Solutions

2QuestionIdentifying Slope and Y-Intercept AI Generate Add Questions SummaryAssessment Practice

4 marks~6 minCriterion D

A delivery drone's battery charge

C

(percent) decreases linearly with horizontal distance

d

(km) from its base. At

d = 1

km the charge reads

2.5\%

; at

d = 4

km the charge reads

1.25\%

Calculate the slope of the line passing through

(1,\ 2.5)

and

(4,\ 1.25)

. [1]

Determine the equation of the line in the form

C = md + b

. [2]

Interpret what

b

represents in this context, and justify whether this model should be used to predict battery charge over a long-distance flight. [1]

Solutions

3QuestionParallel and Perpendicular Lines IntroductoryConcept Practice

2 marks~3 minCriterion C

A city planner is designing two straight roads on a coordinate grid. Road A follows the equation

y = 2x + 1

.

Road B must be built perpendicular to Road A, passing through the point

(4, -1)

Deduce the slope of Road B. [1]

The planner claims Road B can be written as

y = -\dfrac{1}{2}x + 1

. Justify whether this equation correctly represents Road B. [1]

Solutions

4QuestionParallel and Perpendicular Lines IntroductoryAssessment Practice

4 marks~6 minCriterion B

An urban planner is designing a pedestrian grid. Two straight paths must meet at a perfect right angle to satisfy accessibility regulations.

The four candidate path pairs are:

Pair 1:

y = 2x + 1

and

y = -\dfrac{1}{2}x + 3

Pair 2:

y = 3x - 2

and

y = -\dfrac{1}{3}x + 5

Pair 3:

y = x + 4

and

y = -x - 1

Pair 4:

y = 4x

and

y = -\dfrac{1}{4}x + 2

For each pair, calculate the product of the two slopes. State what you observe. [1]

The angle

\theta

between two lines with slopes

m_1

and

m_2

is given by

\tan\theta = \left|\frac{m_1 - m_2}{1 + m_1 m_2}\right|

Apply this formula to Pairs 1 and 3. Deduce the value of

\theta

for each, and explain why the formula behaves as it does for these two pairs. [2]

The accessibility regulation requires paths to meet at exactly 90°. Justify whether all four pairs satisfy this regulation, and state the general algebraic condition that guarantees perpendicularity. [1]

Solutions

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