Use the image to answer the 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.
(1 point)
To find the equation of the line through the origin, we first need to determine the slope (m) of the line. To do this, we can compare the change in y-coordinates to the change in x-coordinates between any two points on the line.
Between the points (3, 1) and (6, 2), the change in y-coordinates is 2 - 1 = 1, and the change in x-coordinates is 6 - 3 = 3.
So, the slope (m) of the line is 1/3.
Therefore, the equation of the line through the origin is y = 1/3x.
To find the equation of the line, we need to determine the slope (m) of the line.
First, let's identify two points on the line. From the given graph, we can see that the line passes through the points (3, 1) and (9, 3).
Next, we can use the formula for slope:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates of the two points:
m = (3 - 1) / (9 - 3)
= 2 / 6
= 1/3
Now, we have the slope (m) of the line.
Given that the line passes through the origin (0, 0), the equation of the line y = mx is:
y = (1/3)x