Question

17 chaque année, la mère de chloé mesure la taille de sa fille le jour de son anniversaire. représente les données du tableau à l’aide d’un diagramme à ligne brisée.

année	2014	2015	2016	2017	2018	2019	2020	2021	2022

Explanation:

To create a broken - line graph (diagramme à ligne brisée) from the given data, we follow these steps:

Step 1: Prepare the coordinate system

• Horizontal axis (x - axis): Represent the years. Mark the years 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022 evenly along the x - axis.
• Vertical axis (y - axis): Represent the height (Taille) in centimeters. Determine a suitable scale. Since the heights range from 47 cm to 137 cm, we can set the scale such that each unit on the y - axis represents, for example, 10 cm. So we mark the y - axis with values 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140 (or a more appropriate scale depending on the size of the graph paper).

Step 2: Plot the data points

• For the year 2014 and height 47 cm: Find the position on the x - axis corresponding to 2014 and the position on the y - axis corresponding to 47 cm. Mark the point (2014, 47).
• For 2015 and 71 cm: Mark the point (2015, 71).
• For 2016 and 88 cm: Mark the point (2016, 88).
• For 2017 and 98 cm: Mark the point (2017, 98).
• For 2018 and 109 cm: Mark the point (2018, 109).
• For 2019 and 114 cm: Mark the point (2019, 114).
• For 2020 and 121 cm: Mark the point (2020, 121).
• For 2021 and 129 cm: Mark the point (2021, 129).
• For 2022 and 137 cm: Mark the point (2022, 137).

Step 3: Draw the broken line

• Connect the consecutive points with straight line segments. Start from the point (2014, 47) and draw a line to (2015, 71), then from (2015, 71) to (2016, 88), and so on, until you connect (2021, 129) to (2022, 137).

If we were to analyze the growth rate between two consecutive years, for example, between 2014 and 2015:

Step 1: Identify the heights

• Height in 2014 ($h_{2014}$) = 47 cm
• Height in 2015 ($h_{2015}$) = 71 cm

Step 2: Calculate the growth amount

The growth amount $\Delta h=h_{2015}-h_{2014}=71 - 47=24$ cm

Step 3: Calculate the growth rate (if we consider the time period as 1 year)

The growth rate $r = \frac{\Delta h}{h_{2014}}\times100\%=\frac{24}{47}\times100\%\approx51.06\%$

(This is just an example of an additional analysis. The main task was to represent the data as a broken - line graph)

If the question was to create the graph, the final answer is the graph constructed by following the above steps of plotting the points and connecting them with line segments. If it was about analyzing the growth, the answer would be the calculated growth rate (or growth amount) depending on the specific question. Since the original question was about representing the data with a broken - line graph, the answer is the graph with points (2014, 47), (2015, 71), (2016, 88), (2017, 98), (2018, 109), (2019, 114), (2020, 121), (2021, 129), (2022, 137) connected by line segments.

Answer:

To create a broken - line graph (diagramme à ligne brisée) from the given data, we follow these steps:

Step 1: Prepare the coordinate system

• Horizontal axis (x - axis): Represent the years. Mark the years 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022 evenly along the x - axis.
• Vertical axis (y - axis): Represent the height (Taille) in centimeters. Determine a suitable scale. Since the heights range from 47 cm to 137 cm, we can set the scale such that each unit on the y - axis represents, for example, 10 cm. So we mark the y - axis with values 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140 (or a more appropriate scale depending on the size of the graph paper).

Step 2: Plot the data points

• For the year 2014 and height 47 cm: Find the position on the x - axis corresponding to 2014 and the position on the y - axis corresponding to 47 cm. Mark the point (2014, 47).
• For 2015 and 71 cm: Mark the point (2015, 71).
• For 2016 and 88 cm: Mark the point (2016, 88).
• For 2017 and 98 cm: Mark the point (2017, 98).
• For 2018 and 109 cm: Mark the point (2018, 109).
• For 2019 and 114 cm: Mark the point (2019, 114).
• For 2020 and 121 cm: Mark the point (2020, 121).
• For 2021 and 129 cm: Mark the point (2021, 129).
• For 2022 and 137 cm: Mark the point (2022, 137).

Step 3: Draw the broken line

• Connect the consecutive points with straight line segments. Start from the point (2014, 47) and draw a line to (2015, 71), then from (2015, 71) to (2016, 88), and so on, until you connect (2021, 129) to (2022, 137).

If we were to analyze the growth rate between two consecutive years, for example, between 2014 and 2015:

Step 1: Identify the heights

• Height in 2014 ($h_{2014}$) = 47 cm
• Height in 2015 ($h_{2015}$) = 71 cm

Step 2: Calculate the growth amount

The growth amount $\Delta h=h_{2015}-h_{2014}=71 - 47=24$ cm

Step 3: Calculate the growth rate (if we consider the time period as 1 year)

The growth rate $r = \frac{\Delta h}{h_{2014}}\times100\%=\frac{24}{47}\times100\%\approx51.06\%$

(This is just an example of an additional analysis. The main task was to represent the data as a broken - line graph)

If the question was to create the graph, the final answer is the graph constructed by following the above steps of plotting the points and connecting them with line segments. If it was about analyzing the growth, the answer would be the calculated growth rate (or growth amount) depending on the specific question. Since the original question was about representing the data with a broken - line graph, the answer is the graph with points (2014, 47), (2015, 71), (2016, 88), (2017, 98), (2018, 109), (2019, 114), (2020, 121), (2021, 129), (2022, 137) connected by line segments.