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: Find two points on the line

From the graph, we can see that when \( x = 0.8 \), \( y = 1 \) (or we can use the origin \((0,0)\) and another point, say \((0.8, 1)\)).

Step3: Calculate the slope \( k \)

The slope \( k \) is calculated as \( k=\frac{y}{x} \). Using the point \((0.8, 1)\), we have \( k = \frac{1}{0.8}=\frac{10}{8}=\frac{5}{4} = 1.25\).

Step4: Write the equation

Substituting \( k = \frac{5}{4} \) into \( y = kx \), we get \( y=\frac{5}{4}x \) (or \( y = 1.25x \)).

Answer:

\( y = \frac{5}{4}x \) (or \( y = 1.25x \))