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.
(1 point)
To find the equation of the line y = mx through the origin, we can use the slope-intercept form of a line, y = mx + b. Since the line passes through the origin (0, 0), this means that the y-intercept, b, is 0.
To find the slope, m, we can identify two points on the line. From the graph, we can see that the line passes through the points (1, 5) and (2, 10).
Using the formula for slope, m = (y2 - y1) / (x2 - x1), we can calculate the slope:
m = (10 - 5) / (2 - 1)
m = 5 / 1
m = 5
Therefore, the equation of the line y = mx through the origin is y = 5x.