3.2.3 Recognizing, interpreting graphs

• Where does the directly proportional graph intersect the origin?

  At (0,0)
• How many slices of cake does each person get if there are 12 people sharing the cake equally?


  1
• What is the maximum amount of cheese shown in the graph?

  5 kg
• In direct proportion, if one quantity decreases, the other quantity increases.

  False
• How much does someone in the GB earn per hour, according to the example in the study material?

  £10
• What are the key features of the inversely proportional graph?

  • Algebraic form: y = k/x^n
  • Always a reciprocal graph
  • One smooth curve
  • Located in the first quadrant only
  • Does not touch any axis
• What is the shape of a direct proportion graph?

  Straight line
• What happens to one quantity in direct proportion when another quantity doubles?

  It also doubles
• What is the shape of an inverse proportion graph?

  Smooth curve
• What are the two types of proportional relationships studied at GCSE?

  Direct proportion and inverse proportion
• Arrange the following pairs of hours worked and earnings in ascending order of earnings:

  1️⃣ 1 hour, £10

  2️⃣ 2 hours, £20

  3️⃣ 3 hours, £30
• What are the lines called that an inverse proportion curve approaches but never touches?

  Asymptotes
• What are the key features of a directly proportional graph?

  • Algebraic form: y = kx
  • Always a straight line graph
  • Positive gradient, k
  • Intersects the origin (0, 0)
• How many slices of cake does each person get if there are 2 people sharing the cake equally?

  6
• What is the algebraic form of a directly proportional relationship?

  y = kx
• What happens to the number of slices per person when the number of people sharing a fixed cake increases in inverse proportion?

  It decreases
• Arrange the table values in descending order of slices per person

  1️⃣ 12

  2️⃣ 6

  3️⃣ 4

  4️⃣ 3

  5️⃣ 2

  6️⃣ 1
• What are the key features of an inversely proportional graph?

  • Algebraic form: y = k/x
  • Always a reciprocal graph
  • One smooth curve
  • Located in the first quadrant only
  • Does not touch any axis
• What is the relationship between the amount of cheese and its cost shown in the graph?

  The cost of cheese increases linearly as the amount of cheese increases
• In the cheese-cost graph, what happens to the cost as the amount of cheese increases?

  Increases consistently
• What general trend can be observed regarding the relationship between height and weight based on the bar chart?

  As height increases, weight also tends to increase.
• According to the chart, what is the weight of a student who is 155 cms tall?

  45 Kg
• If the algebraic form of a proportional relationship is y = 3x, what is the value of the constant of proportionality, k?

  3
• What type of graph can the directly proportional graph be?

  It can be a straight line, quadratic, cubic graph or graph in the form y = √x
• How do the graphs of directly proportional and inversely proportional relationships differ?

  Directly proportional is a straight line, inversely proportional is a smooth curve
• According to the chart, what height has the highest weight?

  170 cms
• According to the chart, what is the height of a student who weights 58 Kg?

  170 cms
• How can you calculate the cost of any amount of cheese using the information in the graph?

  • The cost of cheese increases by $10 for every 1 kg increase in amount
  • So to calculate the cost for any amount, multiply the amount (in kg) by $10
• Match the number of people with the slices per person:

  1 ↔️ 12

  2 ↔️ 6

  3 ↔️ 4

  4 ↔️ 3

  6 ↔️ 2

  12 ↔️ 1
• What type of relationship does an inverse proportion graph show?

  Reciprocal relationship
• What is the algebraic form of the directly proportional graph?

  y = kx^n
• According to the chart, which height corresponds to the lowest weight?

  150 cms
• According to the chart, is the relationship between height and weight positive or negative?

  Positive
• What type of proportion relationship is demonstrated between height and weight in the graph?

  Direct proportion
• What is the fundamental difference between direct and inverse proportion graphs?

  Their fundamental relationship
• What does the inverse proportion graph illustrate about the variables?

  Opposite directions
• What is the cost of 1 kg of cheese?

  $10
• According to the chart, what is the weight of a student who is 150 cms tall?

  42 Kg
• What type of graph does direct proportion form?

  Linear
• How many slices of cake does each person get if there is only 1 person sharing the cake?

  12