Analyzing Graphs of Linear Equations in Real Life Situation

This graph shows the change of depth, d, of water against time, t, as a container is filled at a constant rate.

Which of these is the container?

• 
• 
• 
• 

Tom cycles to his Grandmother’s house, which is 12km from his home. He stays there for 45 minutes. The distance-time graph shows his journey. Work out the fastest speed that Tom cycles at on his way to his grandmother’s house.

• 16 km/h

• 8 km/h

• 4 km/h

• 12 km/h

What is represented by the gradient of the line?

• Distance

• Speed

• Time

• Change in time

Write down, in words, the units represented by the gradient of the line.

• Metres per minute

• m/m

• Miles per hour

• Metres

The graph shows the costs of lotion C, represented by line C, and lotion D, represented by line D. Decide of the following statements are true or false.

Groups:

(a) TRUE

,

(b) FALSE

• Lotion D costs more than Lotion C

• Lotion C cost more than Lotion D

• The cost of lotion D is $2.00 per ounce.

• The cost of lotion C is $0.50 per ounce.

• A

• B

• C

• D

The monthly cost of renting a laptop is shown in the graph. Which equation best represents the cost, y, of renting the laptop for, x, months?

• y = 45x

• y = 35x + 45

• y = 65x + 45

• y = 20x + 45

Identify the nature of solution from the graph given.

• Consistent and unique solution

• Inconsistent : No solution

Choose the correct equation for the given graph.

• y = x + 2

• y = 4 + x

• y = x - 2

• y = 4 - x

Answer explanation

As we can see in the graph that the line is intersecting x axis at 2 and y axis at -2. So here we have got two points (2, 0) and (0, -2). Now let's substitute these points in y = x - 2 (2, 0) In LHS, y = 0 In RHS, x - 2 = 2 - 2 = 0 So, LHS = RHS (0, -2) In LHS, y = -2 In RHS, x - 2 = 0 -2 = -2 So, LHS = RHS Therefore, The graph in the figure is of the equation y = x - 2 and option 3 is the correct answer.

When is the graph decreasing?

• 40 - 60

• 0-10

• 10-40