Question

a. The constant of proportionality is:

b. Write an equation that represents the linear graph:

c. This is a proportional relationship because the graph shows:

Answer 1

To address your questions, let's break them down into parts.

a. **The constant of proportionality** is the ratio between the two quantities that are being compared, often denoted as \( k \). It's calculated by taking one value and dividing it by its corresponding value in a proportional relationship. For example, if you have two quantities \( y \) and \( x \), and you see that \( y = kx \), then \( k \) is your constant of proportionality.

b. **The equation that represents the linear graph** typically takes the form of \( y = mx + b \), where:
- \( m \) is the slope of the line (rate of change),
- \( b \) is the y-intercept (the value of \( y \) when \( x = 0 \)).
If the graph is through the origin (0,0), it simplifies to \( y = kx \), indicating a proportional relationship.

c. **This is a proportional relationship because the graph shows** a straight line that passes through the origin (0,0). All points on the line maintain a constant ratio between the dependent and independent variables, demonstrating that as one quantity increases, the other does so in a consistent manner according to the constant of proportionality.

If you have specific values or a graph in mind, feel free to share for a more tailored response!