Question

Find the equation of the line y=mx
through the origin that describes the proportional relationship
first point (1, 4) second point (2, 8)

Answer 1

To find the equation of the line \( y = mx \) that passes through the origin and describes a proportional relationship between the points (1, 4) and (2, 8), we first need to determine the slope \( m \).

In a proportional relationship, if \( (x_1, y_1) = (1, 4) \) and \( (x_2, y_2) = (2, 8) \), we can compute the slope \( m \) using the coordinates of one of the points:

Using the first point (1, 4):
\[
m = \frac{y_1}{x_1} = \frac{4}{1} = 4
\]

Now, using the second point (2, 8) to confirm the slope:
\[
m = \frac{y_2}{x_2} = \frac{8}{2} = 4
\]

Since we calculated the same slope from both points, we can conclude that the slope \( m \) is indeed 4.

Therefore, the equation of the line is:
\[
y = 4x
\]

This describes the proportional relationship through the origin for the given points.