Question

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

Explanation:

Step1: Recall proportional relationship formula

A proportional relationship has the form \( y = kx \), where \( k \) is the constant of proportionality (slope). To find \( k \), we can use two points on the line. The graph passes through the origin \((0,0)\) and let's find another point. From the graph, when \( x = 10 \), \( y = 2 \) (or we can check other points, but let's use \( (10,2) \)).

Step2: Calculate the slope \( k \)

The formula for slope \( k \) is \( k=\frac{y}{x} \). Using the point \((10,2)\), we substitute \( x = 10 \) and \( y = 2 \) into the formula: \( k=\frac{2}{10}=\frac{1}{5}=0.2 \).

Step3: Write the equation

Substitute \( k=\frac{1}{5} \) into \( y = kx \), so the equation is \( y=\frac{1}{5}x \) (or \( y = 0.2x \)).

Answer:

\( y=\frac{1}{5}x \) (or \( y = 0.2x \))