Question

ii. write an equation in the form of y=ax or y=x+a that describes the relationship between x and y.
★ a.
distance adriana traveled
distance (miles)
200
150
100
50
0
2 4 6 8 10
time (hours)
b.
calories burned rowing
calories burned
200
150
100
50
0
15 30 45 60
time (minutes)

Explanation:

Step1: Analyze graph A

For graph A, when \(x = 2\), \(y=100\). We assume the equation is \(y = ax\). Substitute the values of \(x\) and \(y\) into the equation: \(100=a\times2\), then \(a = 50\). The equation for graph A is \(y = 50x\).

Step2: Analyze graph B

For graph B, when \(x = 15\), \(y = 50\). Assume the equation is \(y=ax\). Substitute \(x\) and \(y\) values: \(50=a\times15\), so \(a=\frac{10}{3}\). But looking at the non - linear pattern of the graph, we note that it is not a simple linear relationship \(y = ax\) or \(y=x + a\) for the whole graph. However, if we consider the first linear part, the equation for the first linear segment (from \(x = 0\) to \(x=15\)) is \(y=\frac{10}{3}x\).

Answer:

A. \(y = 50x\)
B. For the first linear part \(y=\frac{10}{3}x\)