Question

name: jayleigh s. block: btw equation write an equation to represent the situation. label each part. table (x) (y) $\frac{y}{x}$ 0 0 1 3 $\frac{1}{3}$ 2 6 3 9 4 12 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: Identify the relationship

We observe that when $x = 1,y = 3$; when $x=2,y = 6$; when $x = 3,y=9$ and when $x=4,y = 12$. The ratio $\frac{y}{x}$ is always 3. The general form of a proportional - relationship equation is $y=kx$, where $k$ is the constant of proportionality.

Step2: Write the equation

Since the constant of proportionality $k = 3$, the equation representing the situation is $y = 3x$. Here, $y$ is the dependent variable, $x$ is the independent variable, and 3 is the constant of proportionality.

Step3: Explain proportionality

The graph is proportional because the ratio of $y$ to $x$ (the slope) is constant for all non - zero values of $x$. For every increase in $x$ by 1 unit, $y$ increases by 3 units. The equation $y = 3x$ is in the form $y=kx$ (where $k = 3$), and the graph of this equation is a straight line passing through the origin $(0,0)$.

Step4: Interpret a point

Let's take the point $(2,6)$. In the situation, if $x$ represents a certain quantity (for example, the number of items), then when there are 2 items ($x = 2$), the corresponding value of $y$ (which could be the cost, for example) is 6. So it means that for 2 units of the quantity $x$, the value of $y$ is 6.

Step5: Highlight the unit rate

In the table, the unit rate is the value of $\frac{y}{x}$, which is 3 for all non - zero $x$ values. In the graph, the unit rate is the slope of the line $y = 3x$, which is 3. In the equation $y=3x$, the coefficient of $x$ (3) is the unit rate.

Answer:

Equation: $y = 3x$; The graph is proportional because $\frac{y}{x}$ is constant and the line passes through the origin. For the point $(2,6)$, it means when $x = 2$, $y = 6$. The unit rate is 3 in the table ($\frac{y}{x}$ values), in the graph (slope), and in the equation (coefficient of $x$).