sanjays family has owned a tree farm for 75 years. because they keep excellent records, sanjay can find out…

Explanation:

Step1: Find the linear - equation

The equation of the line of best - fit in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given $m = 4.3$ and $b = 0.2$, the equation is $y=4.3x + 0.2$, where $x$ is the diameter of the tree in inches and $y$ is the age of the tree in years.

Step2: Evaluate the first statement

When $x = 15$, $y=4.3\times15 + 0.2=64.5+0.2 = 64.7\approx65$. So the first statement is True.

Step3: Evaluate the second statement

When $y = 51$, we solve the equation $51=4.3x + 0.2$ for $x$. First, subtract $0.2$ from both sides: $51 - 0.2=4.3x$, so $4.3x = 50.8$. Then $x=\frac{50.8}{4.3}\approx11.81\neq9.5$. So the second statement is False.

Step4: Evaluate the third statement

If the diameter changes from $x_1$ to $x_2=x_1 + 10$, then $y_1=4.3x_1+0.2$ and $y_2=4.3(x_1 + 10)+0.2=4.3x_1+43 + 0.2$. The difference $y_2 - y_1=(4.3x_1+43 + 0.2)-(4.3x_1+0.2)=43$. So a 10 - inch increase in diameter corresponds to a 43 - year increase in age. The third statement is True.

Step5: Evaluate the fourth statement

When $x_1 = 8$, $y_1=4.3\times8+0.2=34.4 + 0.2=34.6$. When $x_2 = 32$, $y_2=4.3\times32+0.2=137.6+0.2 = 137.8$. $\frac{y_1}{y_2}=\frac{34.6}{137.8}\approx0.25\neq0.5$. So the fourth statement is False.

Answer:

A tree with a diameter of 15 inches is approximately 65 years old: True A tree that is 51 years old would have a diameter of about 9.5 inches: False A 10 - inch increase in diameter corresponds to a 43 - year increase in age: True A tree with a diameter of 8 inches is about half the age of a tree with a diameter of 32 inches: False