7G_Graphs

Graphs

​Unit 11

​Learning Objectives

​After studying this topic, students are able to:

​• represent situations in words or as linear functions

​• plot graphs of linear functions

​• learn how to recognize lines parallel to the x-axis or y-axis

​• interpret graphs related to rates of change

Multiple Choice

What is the coordinate of this point?

• (8, 2)

• (2, 7)

• (2, 8)

• (8, 3)

Multiple Choice

Given an expression $$2x-5$$  

What is the value of the expression, when $$x=1$$  ?

• 3

• -3

• 16

• -8

​11.1 Functions

​A function shows the relationship between two variables.

You often use x and y to represent two variables, but you can use other letters.

​

​Example:

Maryam is 6 years older than his brother Jamal.

​ m = j + 6

​So, when Jamal is 12 years old, Maryam will be:

​ m = 12 + 6 = 18 years old

Multiple Choice

Lilah's mass is $$\frac{3}{4}$$  of the mass of Abdul.

If Abdul's mass is 40 kg, what is the mass of Lilah?

• 30

• 40

• 50

• 60

Multiple Choice

The relationship between US Dollar (x) and Libyan Dinar (y) is $$y=1.5x$$  .

How much Libyan Dinar will you get, if you exhange US $100 ?

• $15

• $150

• $1500

• $15000

​11.2 Graph of functions

​Given a function y = x + 3.

When x = ​2, then y = 2 + 3 = 5

​When x = -4, then y = -4 + 3 = -1

​

​You can display values of x and the corresponding values of y in a table

​11.2 Graph of functions

​Given a function y = x + 3.

​

​

​

Q: Is the point (5,9) located on the line?

​

Check:

y = x + 3

when x=5, y=5+3=8,

So, the point (5,8) is on the line, but

the point (5,9) is NOT on the line. ​

​

​

Multiple Choice

Given a line with the function $$y=x-2$$  .

Which of the following points is NOT located on the line?

• (0, -2)

• (2, 0)

• (3, -1)

• (4, 2)

​11.3 Lines parallel to the axes

​A and B are on a line parallel to

​the y-axis. The line is x = 4.

​

​​C and D are on a line parallel to

​the y-axis. The line is x = -2.

​​

A and D are on a line parallel to

​the x-axis. The line is y = 2.

​​

B and C are on a line parallel to

​the x-axis. The line is y = -3.

​

Multiple Choice

What is the equation of this line?

• x = -5

• y = -5

• x - y = -5

• x + y = -5

Multiple Choice

Which of these is the equation of the line that passes through

(–2, 2), (5, 2) and (–1, 2)?

• y = -2

• x = 5

• y = 2

• x = -1

​11.4 Interpreting graphs

Graphs can show how the value of variable changes with time.

​

Example:​

​This graph shows the distance

travelled by a runner in a 5 km race.

Multiple Choice

How long does the runner take to run the 5 km race?

• 5 minutes

• 10 minutes

• 15 minutes

• 20 minutes

Multiple Choice

How far has the runner gone after 5 minutes?

• 1 km

• 1.6 km

• 2 km

• 3 km

Multiple Choice

The graph shows a 10 km race run by Sachita and Anandhu.

Who ran at the same speed for 10 km?

• Sachita

• Anandhu

Multiple Choice

Which was the faster part of the journey?

• Between 7 am and 8 am 

• Between 8:00 am and 8:30 am

Multiple Choice

A plane flies from New York to Brussels.

The graph shows the distance left to travel during the flight.

How many kilometres has the plane flown after five hours?

• 2500 km 

• 3500 km

• 2000 km

• 1000 km