Question

A scientist created a scatterplot to display the height of a plant over a 12-day period. Plant Height A graph has days on the x-axis and height (inches) on the y-axis. A trend line goes through points (5, 3) and (12, 7). Which is the equation of the trend line that is shown? y = StartFraction 1 Over 7 EndFraction x + StartFraction 4 Over 7 EndFraction y = StartFraction 1 Over 7 EndFraction x + StartFraction 16 Over 7 EndFraction y = StartFraction 4 Over 7 EndFraction x minus StartFraction 1 Over 7 EndFraction y = StartFraction 4 Over 7 EndFraction x + StartFraction 1 Over 7 EndFraction

Answer 1

Answer:

D

Step-by-step explanation:

Answer 2

Answer:

The correct option is (D) $y=\frac{4}{7}\ x+\frac{1}{7}$.

Step-by-step explanation:

The two-point form for the equation of straight line is:

$(y-y_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\ (x-x_{1})$

The two points provided are:

A = (5, 3)

B = (12, 7)

Compute the equation of the trend line as follows:

$(y-y_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\ (x-x_{1})\\\\(y-3)=\frac{7-3}{12-5}\ (x-5)\\\\(y-3)=\frac{4}{7}\ (x-5)\\\\y-3=\frac{4}{7}\ x-\frac{20}{7} \\\\y=\frac{4}{7}\ x-\frac{20}{7}+3\\\\y=\frac{4}{7}\ x+\frac{-20+21}{7}\\\\y=\frac{4}{7}\ x+\frac{1}{7}$

Thus, the equation of the trend line is $y=\frac{4}{7}\ x+\frac{1}{7}$.

The correct option is (D).