Find the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
4,1 8,2
To find the equation of the line through the origin that describes the proportional relationship shown in the graph with the points (4,1) and (8,2), we need to determine the slope (m) of the line.
The slope (m) of a line passing through two points, (x1, y1) and (x2, y2), is calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (4,1) and (8,2), we can substitute the values into the formula:
m = (2 - 1) / (8 - 4)
m = 1 / 4
m = 1/4
Now that we have the slope (m), we can substitute it into the equation of a line, y = mx, where m is the slope.
The equation of the line is:
y = (1/4)x
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