Question

1. the table shows the ages and weights of six kittens.

age (weeks) 2 4 6 8 10
weight (oz) 8 14 23 31 42
write the equation of the line that models the situation
do the data show a positive or a negative correlation?

Explanation:

Step1: Calculate the slope

Let $x$ be the age (weeks) and $y$ be the weight (oz). We take two points $(x_1,y_1)=(2,8)$ and $(x_2,y_2)=(4,14)$. The slope $m$ of the line is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$.
$m=\frac{14 - 8}{4 - 2}=\frac{6}{2}=3$

Step2: Calculate the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ and rewrite it in slope - intercept form $y=mx + b$. Substitute $m = 3$, $x = 2$ and $y = 8$ into $y=mx + b$.
$8=3\times2 + b$
$8 = 6 + b$
$b=8 - 6=2$

Step3: Write the equation of the line

The equation of the line in slope - intercept form is $y=mx + b$. Substituting $m = 3$ and $b = 2$, we get $y = 3x+2$.

Step4: Determine the correlation

As the age ($x$) increases, the weight ($y$) also increases. So the data show a positive correlation.

Answer:

The equation of the line is $y = 3x+2$. The data show a positive correlation.