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The equation of a straight line can be identified by two possible ways:

- When a gradient and one point lying on it is given
- When two points lying on it are given

**Gradient** is another name for the slope of the line (Maths is fun, 2016).

The gradient (m) of a line can be calculated using the formula:

$$

Gradient (m) =

Change in y-axis

Change in x-axis

For example, if we have two points (1, 2) and (4, 8), we can calculate the gradient as follows:

$$

Change in y-axis (Δy) = 8 - 2 = 6

Change in x-axis (Δx) = 4 - 1 = 3

Now, plug these values into the gradient formula:

$$

Gradient (m) =

6

3

= 2

So, the gradient (m) is 2.

The intercept (c) is the point where the line crosses the y-axis.

In the equation of a line, it is represented as:

$$

y = mx + c

For example, if we know the gradient (m) is 4 and a point (2, 6) lies on the line, we can find the intercept (c) as follows:

$$

y = mx + c

6 = 4 * 2 + c

6 = 8 + c

c = 6 - 8

c = -2

So, the equation of the line is:

y = 4x - 2

When two points (2, 8) and (4, 4) are given, we can calculate the gradient (m) as shown earlier, which is -2. Then, using one of the points, for example (4, 4), we can find the intercept (c) as follows:

$$

y = mx + c

4 = -2 * 4 + c

4 = -8 + c

c = 4 + 8

c = 12

So, the equation of the line is:

y = -2x + 12

Bar charts are used to represent data in a graphical format.

There are three formats of bar charts:

- Multiple Bar Chart
- Simple Bar Chart
- Component Bar Chart

The chart below represents the sales of different juice flavors (Apple, Mango, Mix Fruit) over the years (2017, 2018, 2019):

Juice Flavor | 2017 (millions) | 2018 (millions) | 2019 (millions) |
---|---|---|---|

Mango | 28 | 26 | 27 |

Mix Fruit | 32 | 34 | 35 |

Apple | 33 | 31 | 30 |

The chart below represents the sales of each flavor (Apple, Mango, Mix Fruit) during the month of January:

Juice Flavor | January Month Sales (millions) |
---|---|

Apple | 2.25 |

Mango | 2.85 |

Mix Fruit | 2.7 |

The chart below represents the sales of each flavor (Apple, Mango, Mix Fruit) during every quarter of the year 2018:

Quarter | 1st Quarter (Millions) | 2nd Quarter (Millions) | 3rd Quarter (Millions) | 4th Quarter (Millions) |
---|---|---|---|---|

Mango | 7.5 | 7 | 6.5 | 7.5 |

Mix Fruit | 8 | 7 | 8.5 | 7.5 |

Apple | 6 | 8 | 7.5 | 6.5 |

A pie chart is a circular chart that represents data in wedge-like sectors.

Each wedge represents a proportionate part of the whole, and the total value of the pie is always 100 percent.

Below is an example of a pie chart that shows the budget allocated to each flavor of the drink:

Juice Flavor | Budget Allocation |
---|---|

Mango | 146,500 |

Mix Fruit | 139,000 |

Apple | 115,500 |

Total | 401,000 |

- Convert the budget figures into percentages:
- Convert the percentages to degrees (360° total):
- Draw the Pie Chart using the calculated degrees.

Juice Flavor | Budget Allocation | Percentage |
---|---|---|

Mango | 146,500 | 36.53% |

Mix Fruit | 139,000 | 34.67% |

Apple | 115,500 | 28.8% |

Juice Flavor | Percentage | Degrees |
---|---|---|

Mango | 36.53% | 131.51° |

Mix Fruit | 34.67% | 124.8° |

Apple | 28.8% | 103.68° |

The following line graph presents the predicted sales during the months of January to June:

Month | Sales forecast (Million) |
---|---|

January | 1 |

February | 1.6 |

March | 2 |

April | 2.2 |

May | 1.8 |

June | 1.7 |

Scatter diagrams are used to represent the relationship between two variables. Below is a scatter graph showing the relationship between sugar price and juice price:

Sugar Price (£) | Mango Juice Price (£) |
---|---|

14.1 | 2.2 |

14.3 | 2.4 |

14.6 | 2.6 |

14.7 | 2.75 |

15 | 3 |

From the scatter graph, we can observe a positive relationship between sugar price and juice price. This suggests that if the sugar prices increase, it will lead to an increase in the price of juice.

Data can be classified into various types:

Qualitative data cannot be measured easily; they are often characteristics or descriptors.

Quantitative data can be easily measured by numbers.

Binomial data can be categorized into two mutually exclusive categories, such as true or false, accept or reject, right or wrong.

Ordinal data follows a natural order and can be ranked.

Nominal data is named or labeled and can be classified into various non-overlapping groups.

Discrete data consists of a finite number of values.

Continuous data can have an infinite number of values within a range.

Here are some examples of the types of data with their respective categories:

Customer feedback (e.g., good or bad)

Sales volume (e.g., number of products sold)

Accept or Reject (e.g., in quality control)

Service ratings on a scale of 1 to 5 (e.g., 1 for poor service, 5 for excellent service)

Preference for pasta types (e.g., Carbonara or Bolognese)

Number of cars sold (e.g., whole numbers)

Height of children (e.g., with decimal values like 152.2, 152.3, etc.)

Here are tables summarizing the types of data for various examples:

Example | Data Type |
---|---|

Customer Feedback | Qualitative |

Example | Data Type |
---|---|

Sales Volume | Quantitative |

Example | Data Type |
---|---|

Accept or Reject (Quality Control) | Binomial |

Example | Data Type |
---|---|

Service Ratings (1 to 5) | Ordinal |

Example | Data Type |
---|---|

Preference for Pasta Types | Nominal |

Example | Data Type |
---|---|

Number of Cars Sold | Discrete |

Example | Data Type |
---|---|

Height of Children | Continuous |

These tables provide a clear categorization of the types of data for each example.

In this mathematical paper, we explored the process of determining the equation of a straight line using two different methods: when the gradient and one point are given, and when two points are given. We also discussed the calculation of the gradient (slope) and the intercept of the line, emphasizing the use of the formula "y = mx + c."

Additionally, we delved into various types of charts and diagrams, including bar charts (multiple, simple, and component), pie charts, line graphs, and scatter graphs, providing real-world examples related to a fruit juice company's sales and budget allocation.

Furthermore, we categorized data into different types, such as qualitative, quantitative, binomial, ordinal, nominal, discrete, and continuous, and provided examples for each category.

This comprehensive exploration of mathematical concepts and data representation serves as a valuable resource for understanding and applying these principles in various mathematical and analytical contexts.

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