Question

Dot one 1,4
Dot two 2,8

Find the equation for the line y = MX through the origin that describes the propositional relationship shown in the graph

Answer 1

To find the equation of the line \( y = mx \) that passes through the origin and describes the relationship between the two points given, we first need to determine the slope \( m \) of the line.

We have two points:
- Point 1: \( (1, 4) \)
- Point 2: \( (2, 8) \)

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

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

Substituting the coordinates of the points:

- \( (x_1, y_1) = (1, 4) \)
- \( (x_2, y_2) = (2, 8) \)

Now substituting in the values:

\[
m = \frac{8 - 4}{2 - 1} = \frac{4}{1} = 4
\]

Thus, the slope \( m \) is \( 4 \).

The equation of the line through the origin can now be written as:

\[
y = 4x
\]

So, the equation for the line describing the relationship between the two points is:

\[
y = 4x
\]