Question

1.The graph shows the height of a plant after a certain amount of time measured in days

Answer 1

To determine whether there is a proportional relationship between both variables (height of plant and number of days), we need to establish the constant of proportionality between both at every point along the line.

Hence, as the height increases from one day to another, the increase in height should be the same proportion for every additional day.

`\begin{gathered} \text{After 10 days, the plant grows to 4cm, that is;} \\ (10,4) \\ \text{After 20 days, it grows to 8.5 cm, that is;} \\ (20,8.5) \\ \text{After 30 days, it grows to 10.5 cm, that is} \\ (30,10.5) \\ \text{There is no constant between the variables at every point given} \\ \text{That is,} \\ (4)/(10)\\e(8.5)/(20)\\e(10.5)/(30) \end{gathered}`

Hence, there is no proportional relationship between the two variables and that is further explained by the fact that the coordinates (shown by the various dots) on the graph cannot form a straight line.