Use the image to answer the question.

Question

An illustration shows a coordinate plane with 4 quadrants. The x-axis ranges from negative 9 to 9 in one unit increments, and the y-axis ranges from negative 11 to 11 in one unit increments. A line is graphed on the plane. An upward slanting line passes through points plotted at left parenthesis 3 comma 1 right parenthesis, left parenthesis 6 comma 2 right parenthesis, and left parenthesis 9 comma 3 right parenthesis.

Write the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph

Answer 1

To write the equation \( y = mx \) for the line that passes through the origin and includes the points (3, 1), (6, 2), and (9, 3), we first need to determine the slope \( m \) of the line.

The slope \( m \) is calculated using the formula: \[ m = \frac{\Delta y}{\Delta x} \] We can use any two points to find the slope. Let's use the points (3, 1) and (6, 2):

1. Change in \( y \): \[ \Delta y = 2 - 1 = 1 \]

2. Change in \( x \): \[ \Delta x = 6 - 3 = 3 \]

Now, plug these values into the slope formula: \[ m = \frac{1}{3} \]

Now that we have the slope \( m \), we can write the equation of the line: \[ y = \frac{1}{3}x \]

Thus, the equation that describes the proportional relationship shown in the graph is: \[ y = \frac{1}{3}x \]