The graph shows the proportional relationship. Derive the equation the equation of the line y=mx through the origin.(1,5), (2,10)
To find the equation of the line that passes through the origin (0,0) and the point (1,5), we need to find the slope (m) of the line first.
The formula for finding the slope of a line passing through two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Using the points (1,5) and (2,10), we can calculate the slope:
m = (10 - 5) / (2 - 1)
m = 5 / 1
m = 5
Now that we have the slope (m=5), the equation of the line through the origin is given by y=mx.
Therefore, the equation of the line passing through the origin and the points (1,5) and (2,10) is:
y = 5x