Graphing Linear Equations

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Graphing Linear Equations — Free MYP4 Mathematics (Extended) 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

2QuestionDrawing Graphs from y = mx + cAssessment Practice

2 marks~3 minCriterion C

A city's water authority monitors daily water usage. A linear model shows that usage increases at a constant rate as population grows. The line passes through

(0,\ 2)

and

(3,\ 5)

, with population (in thousands) on the

x

-axis and daily water usage (in megalitres) on the

y

-axis.

Deduce the gradient

m

and

y

-intercept

c

, and write the equation of the line in the form

y = mx + c

. [1]

The authority warns that usage exceeding 6 megalitres per day risks supply shortages. Justify whether a population of 4000 triggers this warning. [1]

Solutions

3QuestionDrawing Graphs from y = mx + cAssessment Practice

2 marks~3 minCriterion D

A mobile phone plan charges a fixed monthly fee of 10 dollars plus 0.05 dollars per megabyte (MB) of data used. The total monthly cost

C

(in dollars) for

d

MB of data is modelled by

C = 0.05d + 10, \quad 0 \leq d \leq 200.

Construct a graph of

C

against

d

for the given domain. Label both axes and indicate the

C

-intercept. [1]

Critique the linear model's suitability for representing the actual cost of a mobile phone plan, identifying one specific feature of real plans that the model fails to capture. [1]

Solutions

4QuestionIdentifying Slope and Y-Intercept AI Generate Add Questions SummaryAssessment Practice

6 marks~9 minCriterion B

A city planner models road gradients using equations of the form

ax + by = c

, where

x

is horizontal distance and

y

is elevation. Four road segments are recorded:

Segment 1:

2x + 3y = 6

, giving

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

Segment 2:

4x - 2y = 8

, giving

y = 2x - 4

Segment 3:

-3x + 6y = 12

, giving

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

Segment 4:

5x + 5y = 15

, giving

y = -x + 3

Analyse the four segments to describe the relationship between the coefficients

a

b

c

and the slope

m

and

y

-intercept

d

y = mx + d

. [2]

Deduce a general rule expressing

m

and

d

in terms of

a

b

, and

c

. [1]

A proposed road follows

7x - 4y = 20

. Apply your rule to determine the slope and

y

-intercept, then verify by converting the equation to the form

y = mx + d

. [2]

A second road follows

2x + 8y = -16

. The planner states that any road with a slope steeper than

-\dfrac{1}{3}

is unsafe for heavy vehicles. Advise the planner whether this road should be approved for heavy-vehicle use, justifying your answer with a numerical comparison. [1]

Solutions

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