Question

a. use two sets of coordinates to write an equation to describe the relationship.
280 -

m is

-2

y =

x
b. interpret the equation in words.
the hearts resting heart rate is

beats each minute.

Explanation:

Step1: Find the resting heart rate

When \(x = 0\) (resting, no time of physical activity), \(y=0\). But from the data points, when \(x = 4\) minutes, \(y = 280\) heart - beats. The formula for the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(4,280)\). Then \(m=\frac{280 - 0}{4-0}=70\). The resting heart rate is \(70\) beats per minute.

Step2: Write the equation

The slope - intercept form of a line is \(y = mx + b\). Since the line passes through the origin \((b = 0)\) and \(m = 70\), the equation is \(y=70x\).

Step3: Interpret the equation

The equation \(y = 70x\) means that the number of heart - beats \(y\) is directly proportional to the time of physical activity \(x\). The coefficient \(70\) represents the rate at which the heart beats per minute of physical activity.

Answer:

The heart's resting heart rate is \(70\) beats each minute. The equation is \(y = 70x\). The equation \(y=70x\) means that the number of heart - beats \(y\) is directly proportional to the time of physical activity \(x\), and the rate of heart - beats per minute of physical activity is \(70\).