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 1 comma 5 right parenthesis and left parenthesis 2 comma 10 right parenthesis.
The graph shows the proportional relationship. Derive the equation of the line y=mx through the origin.
To find the slope (m) of the line, we use the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates from the points (1, 5) and (2, 10):
m = (10 - 5) / (2 - 1)
m = 5 / 1
m = 5
So the slope of the line is 5.
Since the line passes through the origin (0, 0), we know that the y-intercept is 0. Therefore, the equation of the line is:
y = 5x