(8 ,2) and (4 ,1)
Find the equation of the line y = mx through the origin that describes the proportional relationship shown in the graph.
To find the equation of the line through the origin that describes the proportional relationship between the two points (8,2) and (4,1), we first need to find the slope, m.
The slope formula is:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates of the two points:
m = (1 - 2) / (4 - 8)
m = -1 / -4
m = 1/4
So, the slope, m, is 1/4.
Now, we can plug the slope into the equation of the line y = mx:
y = (1/4)x
Therefore, the equation of the line through the origin that describes the proportional relationship between the two points is y = (1/4)x.