Question

Use the graph to derive the equation y=mx for a line through the origin. Simplify the numerical coefficient, if needed. (1 point) Responses y=8x y equals 8 x y=x y equals x y=3x y equals 3 x y=3/3x y equals Start Fraction 3 over 3 End Fraction x

Answer 1

To derive the equation of a line through the origin in the form \( y = mx \), you need to identify the slope of the line on the graph. However, since I can't see the graph, let's consider the given responses in relation to the typical forms of the linear equation \( y = mx \).

- If the slope \( m \) is 8, the line's equation is \( y = 8x \).
- If the slope \( m \) is 1, the equation simplifies to \( y = x \).
- If the slope \( m \) is 3, the equation is \( y = 3x \).

The options given include potentially simplified forms for these slopes (like \( y = \frac{3}{3}x \), which simplifies to \( y = x \)).

To summarize:
- The line through the origin will have an equation of the form \( y = mx \).
- If the slope is 8, choose \( y = 8x \).
- If the slope is 1, choose \( y = x \).
- If the slope is 3, choose \( y = 3x \).

Given the responses:
1. \( y = 8x \)
2. \( y = x \)
3. \( y = 3x \)
4. \( y = \frac{3}{3}x \) (which simplifies to \( y = x \))

Select the appropriate option based on the slope observed in the graph. If no specific slope is mentioned or shown, you can choose one of the given equations accordingly.