It seems like you are looking to establish a relationship between variables \(x\) and \(y\) that involves a rate of travel over time, along with an understanding of the intercept. Let’s clarify your requirements step by step:
a. “Every minute \(x\) meters are traveled.”
This statement suggests a constant rate of travel, where you could let \(x\) represent time in minutes and the distance traveled in meters would then be proportional to time. If you traveled a certain number of meters \(m\) every minute, your travel distance over time could be represented as a linear function.
b. “Write an equation to show the relationship between \(x\) and \(y\).”
You can express this relationship with the equation:
\[
y = mx
\]
where:
- \(y\) is the total distance traveled (in meters),
- \(m\) is the rate of travel (meters per minute),
- \(x\) is the time traveled (in minutes).
c. “The relationship is linear because the y-intercept is…”
In the equation \(y = mx + b\), the term \(b\) represents the y-intercept, which is the value of \(y\) when \(x = 0\). If you start from a position of 0 meters at time 0, then the y-intercept would be \(0\). Thus, the relationship is linear because the graph of \(y\) as a function of \(x\) results in a straight line, starting from the origin (0,0).
Putting it all together:
- The rate of travel is \(m\) meters per minute.
- The equation showing the linear relationship is \(y = mx\).
- The relationship is linear because the y-intercept is \(0\), indicating no distance traveled when no time has elapsed.
Feel free to provide specific values or terms if you need a more detailed breakdown or a different context!