Question

find the equation that represents the proportional relationship in this graph, for y in terms of x.

Explanation:

Step1: Recall proportional relationship formula

For a proportional relationship, the equation is \( y = kx \), where \( k \) is the constant of proportionality (slope).

Step2: Identify a point on the graph

From the graph, when \( x = 1 \), \( y = 0.7 \) (assuming the end - point is at \( (1, 0.7) \)). We can also check other points. For example, if we consider the general form, we can use the formula for slope \( k=\frac{y}{x} \) (since it passes through the origin \( (0,0) \)).

Step3: Calculate the constant of proportionality \( k \)

Using the point \( (x = 1,y = 0.7) \), substitute into \( y=kx \). We get \( 0.7=k\times1 \), so \( k = 0.7=\frac{7}{10} \) or we can also see from the graph's trend. Another way: if we take the rise over run. Since the line passes through the origin, the slope \( k=\frac{y}{x} \). Let's assume when \( x = 1 \), \( y=0.7 \), so \( k = 0.7 \).

Step4: Write the equation

Substitute \( k = 0.7 \) into \( y=kx \), we get \( y = 0.7x \) or \( y=\frac{7}{10}x \).

Answer:

\( y = 0.7x \) (or \( y=\frac{7}{10}x \))