Question

the table lists data that is exactly linear.
(a) find the slope - intercept form of the line that passes through these data points.
(b) decide if these calculations involve interpolation or extrapolation. predict y when x = - 6.8 and 10.4.
(a) the slope - intercept form of the line that passes through these data points is y = □x+□ (simplify your answers. use integers or decimals for any numbers in the equation.)

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Calculate the slope $m$

The formula for the slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points, say $(x_1,y_1)=(9,89)$ and $(x_2,y_2)=(22,66.9)$. Then $m=\frac{66.9 - 89}{22 - 9}=\frac{- 22.1}{13}=-1.7$.

Step3: Find the y - intercept $b$

We use the point - slope form $y - y_1=m(x - x_1)$ and then convert to slope - intercept form. Using the point $(9,89)$ and $m=-1.7$, we have $y - 89=-1.7(x - 9)$. Expand: $y-89=-1.7x + 15.3$. Then $y=-1.7x+104.3$.

Step4: Predict $y$ when $x=-6.8$

Substitute $x = - 6.8$ into $y=-1.7x + 104.3$. So $y=-1.7\times(-6.8)+104.3=11.56 + 104.3=115.86$.

Answer:

(a) $y=-1.7x + 104.3$
(b) $115.86$