Question

write an equation to represent the situation. label each part. describe in words why your graph is proportional. take any point from the graph and explain what it means in the situation. highlight the unit rate in your table, graph, and equation.

Explanation:

Step1: Find the relationship in the table

Let \(x\) be the values in the first - column (\(1,2,3,4\)) and \(y\) be the values in the second - column (\(3,6,9,12\)). We can observe that \(y = 3x\).

Step2: Determine if it is proportional

A relationship is proportional if it can be written in the form \(y=kx\) (where \(k\) is a non - zero constant). Here \(k = 3\). For any two pairs \((x_1,y_1)\) and \((x_2,y_2)\) in the table, \(\frac{y_1}{x_1}=\frac{y_2}{x_2}\). For example, when \(x_1 = 1,y_1 = 3\) and \(x_2=2,y_2 = 6\), \(\frac{y_1}{x_1}=\frac{3}{1}=3\) and \(\frac{y_2}{x_2}=\frac{6}{2}=3\).

Step3: Interpret a point

Take the point \((2,6)\). In a general context (assuming \(x\) and \(y\) have some real - world meaning), if \(x\) represents the number of items and \(y\) represents the total cost, then the point \((2,6)\) means that when there are 2 items, the total cost is 6 units (could be dollars, etc.).

Step4: Identify the unit rate

The unit rate is the value of \(y\) when \(x = 1\). In the table, when \(x = 1,y = 3\). In the equation \(y=3x\), the coefficient of \(x\) (which is 3) is the unit rate. On a graph of \(y = 3x\), the slope of the line is 3, which is also the unit rate.

Answer:

The equation representing the situation is \(y = 3x\). The graph is proportional because the ratio of \(y\) to \(x\) is constant (\(y/x=3\) for all non - zero \(x\) values in the table). For the point \((2,6)\), it could mean 2 units of something correspond to 6 units of another related quantity. The unit rate is 3, which is the value of \(y\) when \(x = 1\) in the table, the coefficient of \(x\) in the equation \(y = 3x\), and the slope of the graph of \(y=3x\).