Question

The graph shows the proportional relationship. Derive the equation of the line y=mx
through the origin. (1, 5) (2, 10)

Answer 1

In a proportional relationship, the equation of the line through the origin can be expressed in the form \( y = mx \), where \( m \) is the slope of the line.

To find the slope \( m \), you can use any two points on the line. In this case, we have the points \( (1, 5) \) and \( (2, 10) \).

The slope \( m \) is calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the coordinates of the points:

- Let \( (x_1, y_1) = (1, 5) \)
- Let \( (x_2, y_2) = (2, 10) \)

Now, substituting these values into the slope formula:

\[
m = \frac{10 - 5}{2 - 1} = \frac{5}{1} = 5
\]

Now that we have the slope \( m = 5 \), we can write the equation of the line in the form \( y = mx \):

\[
y = 5x
\]

Thus, the derived equation of the line through the origin that represents the proportional relationship is:

\[
\boxed{y = 5x}
\]