Write the equation of the line y =mx through the origin that shows the proportional relationship in the graph. Express your answer as a fraction in simplest form.

(1 point)
Responses

y = 1/3×
1
3
×
y = 1 third times

y =2/3×
2
3
×
y =2 thirds times

y = 5/12×
5
12
×
y = 5 over 12 times

y =2/4×

1 answer

To express the equation of the line through the origin in the form \( y = mx \) where \( m \) represents the slope, we look at the options provided. Each response indicates a different value for \( m \).

We can simplify the fraction \( \frac{2}{4} \) to \( \frac{1}{2} \).

So, let's write out the options for clarity:

\( y = \frac{1}{3}x \)
\( y = \frac{2}{3}x \)
\( y = \frac{5}{12}x \)
\( y = \frac{2}{4}x \) which simplifies to \( y = \frac{1}{2}x \)

Since you need to express it in simplest form, the first three options are already in their simplest form as the fractions cannot be reduced further.

So, you have:

\( y = \frac{1}{3}x \)
\( y = \frac{2}{3}x \)
\( y = \frac{5}{12}x \)
\( y = \frac{1}{2}x \)

Choose the one that fits your graph slope. If confirmed, all of these represent lines passing through the origin where \( y \) varies proportionally with \( x \).

Please select the response that best fits your required slope.