Question

8, 8, 3, 3
Use the graph to derive the equation y = mx for a line through the origin. Simplify the numerical coefficient, if needed.
A. y = 8x
B. y = 3/3 x
C. y = x
D. y = 3x

Answer 1

To derive the equation of a line through the origin (which has the form \( y = mx \), where \( m \) is the slope), we need to calculate the slope using the points given: \( (8, 8) \) and \( (3, 3) \).

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

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

Using the points \( (8, 8) \) as \( (x_1, y_1) \) and \( (3, 3) \) as \( (x_2, y_2) \):

\[
m = \frac{3 - 8}{3 - 8} = \frac{-5}{-5} = 1
\]

Therefore, the slope \( m \) is 1, which gives us the equation:

\[
y = 1x \quad \text{or} \quad y = x
\]

Since the question asks us to simplify the numerical coefficient if needed, we see that \( 1x \) simplifies to just \( x \).

Now, looking at the provided options:

A. \( y = 8x \)
B. \( y = \frac{3}{3}x \) (which simplifies to \( y = x \))
C. \( y = x \)
D. \( y = 3x \)

The correct answer that matches our derived equation \( y = x \) is:

**C. \( y = x \)**