Question

1. using the point (3, 45), find the constant of proportionality k and write an equation that describes the proportional relationship.

Explanation:

Step1: Recall proportional relationship formula

For a proportional relationship, the formula is \( y = kx \), where \( k \) is the constant of proportionality. We know the point \((x, y)=(3, 45)\), so we substitute \( x = 3 \) and \( y = 45 \) into the formula.
\( 45=k\times3 \)

Step2: Solve for k

To find \( k \), we divide both sides of the equation \( 45 = 3k \) by 3.
\( k=\frac{45}{3}=15 \)

Step3: Write the proportional equation

Now that we know \( k = 15 \), we substitute \( k \) back into the proportional relationship formula \( y = kx \). So the equation is \( y = 15x \).

Answer:

The constant of proportionality \( k \) is 15, and the equation describing the proportional relationship is \( y = 15x \).