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.
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)
1 answer