Question

Dot one 4,1
Dot two 8,2

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 goes through the origin (0,0) and describes the proportional relationship between the two given points, we first need to determine the slope \( m \) of the line.

Given the points:
- Dot one: (4, 1)
- Dot two: (8, 2)

We can calculate the slope \( m \) using the formula for the slope between two points:

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

Using our points:
- \( (x_1, y_1) = (4, 1) \)
- \( (x_2, y_2) = (8, 2) \)

Plugging in the values:

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

Now that we have the slope, we can write the equation of the line through the origin:

\[
y = \frac{1}{4} x
\]

So, the equation of the line that describes the proportional relationship between the given points is:

\[
y = \frac{1}{4} x
\]