Find the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.

Question

4,1 8,2

Answer 1

To find the equation of the line through the origin, we need to find the slope of the line.

The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)

Using the coordinates of the points (4,1) and (8,2):
m = (2 - 1) / (8 - 4)
m = 1/4

So, the slope of the line is 1/4.

Since the line passes through the origin, its equation can be written as:
y = mx

Substituting m = 1/4, the equation of the line is:
y = 1/4x