Question

The graph of a proportional relationship contains the point (−12,3) .

What is the corresponding equation?

Enter your answer as a fraction in simplest form by filling in the boxes.
y = $$ x

Answer 1

In a proportional relationship, the equation can be expressed in the form \( y = kx \), where \( k \) is the constant of proportionality.

Given the point \((-12, 3)\), we can find \( k \) by substituting the values of \( x \) and \( y \) into the equation:

\[
3 = k(-12)
\]

To find \( k \), solve for \( k \):

\[
k = \frac{3}{-12} = \frac{3 \div 3}{-12 \div 3} = \frac{1}{-4} = -\frac{1}{4}
\]

Now, we can write the equation of the proportional relationship:

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

So, the equation in fraction form is:

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

You can fill in the boxes as follows:

- The numerator is \(-1\)
- The denominator is \(4\)

Thus, the final answer is:

\( y = -\frac{1}{4} x \)