Question

each point is the measured recessional velocity and distance to a galaxy. use the given line to draw the best trend line to the data. using your best fit line, calculate the rate of the expansion of the universe. rate of the expansion: km/s/mpc

Explanation:

Step1: Recall Hubble's Law

Hubble's Law is $v = H_0d$, where $v$ is the recessional velocity, $d$ is the distance, and $H_0$ is the Hubble - constant (rate of the expansion of the Universe). The slope of the best - fit line of a graph of recessional velocity ($y$ - axis) versus distance ($x$ - axis) gives the Hubble constant.

Step2: Select two points on the best - fit line

Let's assume two points $(x_1,y_1)$ and $(x_2,y_2)$ on the best - fit line. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step3: Calculate the slope

Suppose we have two points $(x_1,y_1)=(2,200)$ and $(x_2,y_2)=(8,800)$ (values estimated from the graph conceptually). Then $m=\frac{800 - 200}{8 - 2}=\frac{600}{6}=100$.

Answer:

100