9. the graph below shows the ages of a group of people along with their maximum heart rates in beats per minute.
a) write an equation for the line of best fit.
b) estimate the maximum heart rate of someone who is 75 years old.

Question

Accepted Answer

# Explanation:
## Step1: Find two points on the line of best fit
Let's assume two points $(x_1,y_1)=(10,210)$ and $(x_2,y_2)=(40,175)$

## Step2: Calculate the slope $m$
The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$
$$
\begin{align*}
m&=\frac{175 - 210}{40 - 10}\
&=\frac{- 35}{30}\
&=-\frac{7}{6}\approx - 1.17
\end{align*}
$$

## Step3: Use the point - slope form $y - y_1=m(x - x_1)$
Using the point $(10,210)$ and $m =-\frac{7}{6}$
$$
\begin{align*}
y-210&=-\frac{7}{6}(x - 10)\
y-210&=-\frac{7}{6}x+\frac{70}{6}\
y&=-\frac{7}{6}x+\frac{70}{6}+210\
y&=-\frac{7}{6}x+\frac{70 + 1260}{6}\
y&=-\frac{7}{6}x+\frac{1330}{6}\
y&=-\frac{7}{6}x+221.67
\end{align*}
$$

## Step4: Estimate for $x = 75$
Substitute $x = 75$ into the equation $y=-\frac{7}{6}x+221.67$
$$
\begin{align*}
y&=-\frac{7}{6}\times75+221.67\
&=- 87.5+221.67\
&=134.17\approx134
\end{align*}
$$

# Answer:
a) The equation of the line of best fit is $y =-\frac{7}{6}x + 221.67$

b) The estimated maximum heart rate for a 75 - year - old is $134$ beats per minute.

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QUESTION IMAGE

Question

Explanation:

Step1: Find two points on the line of best fit

Step2: Calculate the slope \(m\)

Step3: Use the point - slope form \(y - y_1=m(x - x_1)\)

Step4: Estimate for \(x = 75\)

Answer: