Question

an indoor soccer field can be rented for personal use. the total cost for renting the field can be found by using the equation ( y = 225x ). the ( x )-variable is the number of hours the field is being rented, and the ( y )-variable is the total cost, in dollars. which statement is true based on the given equation? the equation shows a linear relationship, but not a proportional relationship. the equation shows a linear relationship and a proportional relationship. the equation does not show a linear relationship or a proportional relationship. the equation shows a proportional relationship, but not a linear relationship.

Explanation:

Step1: Identify linear form

A linear relationship follows $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept. For $y=225x$, $b=0$, so it fits $y=mx$, a linear equation.

Step2: Check proportionality

A proportional relationship has the form $y=kx$ (passes through the origin, $b=0$). Here, $y=225x$ matches this form, so it is proportional.

Answer:

The equation shows a linear relationship and a proportional relationship.