Question

a scatterplot is used to display data where x is the amount of time, in minutes, one member can tolerate the heat in a sauna, and y is the temperature, in degrees fahrenheit, of the sauna which interpretation describes a line of best fit of y = -1.5x + 173 for the data? the member can tolerate a temperature of 173° fahrenheit for 0 minutes the amount of time the member can tolerate the heat in a sauna is 173 minutes the time increased 1.5 minutes for every degree fahrenheit the temperature increased the time decreased 1.5 minutes for every degree fahrenheit the temperature decreased

Explanation:

Step1: Analyze the slope - intercept form of a linear equation

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the given equation \(y=-1.5x + 173\), when \(x = 0\), \(y=173\).

Step2: Interpret the \(y\) - intercept

The \(y\) - intercept \((x = 0)\) gives the value of \(y\) (temperature) when \(x\) (time) is \(0\). That is, when the time \(x = 0\) minutes, the temperature \(y=173^{\circ}\text{F}\).

Step3: Analyze the slope

The slope \(m=-1.5=\frac{\Delta y}{\Delta x}\). The slope represents the rate of change of \(y\) with respect to \(x\). A negative slope means that as \(x\) (time) increases, \(y\) (temperature) decreases. The slope \(m=-1.5\) means that for every 1 - unit increase in \(x\) (time), \(y\) (temperature) decreases by \(1.5\) units.

Answer:

The member can tolerate a temperature of \(173^{\circ}\) Fahrenheit for \(0\) minutes.