Question

describe how you will identify a proportional relationship in a table and a graph. provide examples of each.

Answer 1

A proportional relationship exist between 2 variable where the ratios are similar or equivalent. A proportional relationship always has a constant value which is also called constant of proportionality . In a table to recognise if it is proportional we write those 2 variables as a fraction and reduce them . There after you compare them to see if the ratios or reduced fractions are equivalent.

Example of a table that depicts proportionality is represented below

The table represent x and y value which are 2 variable now let us check if the table above exhibit proportionality.

let us take the ratios of the x and y values and see if the reduced ratio is same for all x and y value in the table.

`\begin{gathered} (x)/(y) \\ (4)/(6)=(2)/(3)=2\colon3 \\ (6)/(9)=(2)/(3)=2\colon3 \\ (8)/(12)=(2)/(3)=2\colon3 \\ (10)/(15)=(2)/(3)=2\colon3 \\ (14)/(21)=(2)/(3)=2\colon3 \end{gathered}`

Notice that the ratio of x to y is the same through out the table. This shows proportionality.

To notice a proportionality on a graph, the graph forms a straight line that run through the origin. example of such graph is

Note we used the value from the table to draw the graph.