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 slope (m) of the line, we need to use two of the given points. Let's use (3,1) and (6,2):
m = (2-1)/(6-3) = 1/3
So the equation of the line y=mx through the origin (0,0) is:
y = (1/3)x
To find the equation of the line that describes the proportional relationship shown in the graph, we can first calculate the slope of the line using two of the given points: (3, 1) and (6, 2).
The slope (m) of a line is calculated using the formula: m = (y2 - y1) / (x2 - x1).
Using the points (3, 1) and (6, 2), we can substitute the values into the formula to find the slope:
m = (2 - 1) / (6 - 3)
m = 1 / 3
So, the slope of the line is 1/3.
Since the line passes through the origin (0, 0), we can use the point-slope form of the equation:
y - y1 = m(x - x1)
Substituting the values of m = 1/3 and (x1, y1) = (0, 0):
y - 0 = (1/3)(x - 0)
y = (1/3)x
Therefore, the equation of the line y = mx that describes the proportional relationship shown in the graph is y = (1/3)x.