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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.

(1 point)
Remaining Attempts : 3
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1 answer

To find the equation of the line \(y = mx\) that describes the proportional relationship shown in the graph, we first need to determine the slope \(m\) using the given points on the line.

The points given are:

  • \( (3, 1) \)
  • \( (6, 2) \)
  • \( (9, 3) \)

We can calculate the slope \(m\) using any two points. Let's use the points \( (3, 1) \) and \( (6, 2) \):

The formula for slope \(m\) is: \[ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \]

Substituting the coordinates: \[ m = \frac{{2 - 1}}{{6 - 3}} = \frac{1}{3} \]

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

Thus, the equation of the line is: \[ y = \frac{1}{3}x \]