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
b.
calories burned rowing

ii. plot the following values on the graph, then write an equation in the form of y = ax or y = x + a that describes the relationship between x and y.

Explanation:

Step1: Analyze graph A

For graph A (Distance Adriana Traveled), we first find two - points on the linear part of the graph. Let's take the points \((2,100)\) and \((4,150)\). The slope \(a\) of the line \(y = ax\) (since it passes through the origin, we assume \(y=ax\) form) is calculated as \(a=\frac{y_2 - y_1}{x_2 - x_1}\).
\[a=\frac{150 - 100}{4 - 2}=\frac{50}{2}=25\]
The equation is \(y = 25x\).

Step2: Analyze graph B

For graph B (Calories Burned Rowing), we note that it is not a linear relationship in the traditional \(y = ax\) or \(y=x + a\) form for the whole graph. But if we consider the last linear - like part from \(x = 45\) to \(x = 60\). Let's take the points \((45,150)\) and \((60,200)\). The slope \(a=\frac{y_2 - y_1}{x_2 - x_1}=\frac{200 - 150}{60 - 45}=\frac{50}{15}=\frac{10}{3}\). Also, when \(x = 45\), \(y = 150\). We can write the equation in the point - slope form \(y - y_1=a(x - x_1)\), substituting \(x_1 = 45,y_1 = 150,a=\frac{10}{3}\).
\[y-150=\frac{10}{3}(x - 45)\]
\[y-150=\frac{10}{3}x-150\]
\[y=\frac{10}{3}x\]

Answer:

A. \(y = 25x\)
B. \(y=\frac{10}{3}x\)