Graphing Linear Equations

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Graphing Linear Equations — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionParallel 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

2QuestionDrawing Graphs from y = mx + cAssessment Practice

4 marks~6 minCriterion D

A company purchases a delivery van for 40 000 dollars. The van loses 3 500 dollars in value each year. The value of the van after

x

years is modelled by:

V = 40000 - 3500x

Calculate the value of the van after 4 years. [1]

Construct a graph of

V

against

x

for

0 \leq x \leq 8

. Label both axes with their quantities and units, and indicate a clear scale. [2]

The company plans to sell the van once its value falls below 15 000 dollars. Using your graph or the equation, deduce the earliest year in which the van should be sold, then advise the company whether the linear model is a reliable basis for this decision. [1]

Solutions

3QuestionDrawing Graphs from y = mx + cConcept Practice

2 marks~3 minCriterion A

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

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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