Question

the table lists data that is exactly linear. (a) find the slope - intercept form of the line that passes through these data points. decide if these calculations involve interpolation or extrapolation. predict y when x = - 6.8 and 10.4. (b) the slope - intercept form of the line that passes through these data points is y = - 1.7x+104.3. use integers or decimals for any numbers in the equation. (a) simplify your answers. (b) predict y when x = - 6.8. (simplify your answer. round to the nearest hundredth.) y = 115.86 predict y for this value of x as an example of the following? interpolation extrapolation predict y when x = 10.4. (simplify your answer. round to the nearest hundredth.) y = □

Explanation:

Step1: Find the slope - intercept form $y = mx + b$

We have two points say $(x_1,y_1)=(9,89)$ and $(x_2,y_2)=(22,66.9)$. The slope $m$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{66.9 - 89}{22 - 9}=\frac{-22.1}{13}=- 1.7$.
Using the point - slope form $y - y_1=m(x - x_1)$ with $(x_1,y_1)=(9,89)$ and $m=-1.7$, we get $y-89=-1.7(x - 9)$. Expanding, $y-89=-1.7x+15.3$, so $y=-1.7x + 104.3$.

Step2: Predict $y$ when $x=-6.8$

Substitute $x = - 6.8$ into the equation $y=-1.7x + 104.3$. Then $y=-1.7\times(-6.8)+104.3=11.56 + 104.3=115.86$. Rounding to the nearest hundredth, $y = 115.86$.

Step3: Predict $y$ when $x = 10.4$

Substitute $x = 10.4$ into the equation $y=-1.7x + 104.3$. Then $y=-1.7\times10.4+104.3=-17.68+104.3 = 86.62$. Rounding to the nearest hundredth, $y = 86.62$.

Answer:

When $x=-6.8$, $y = 115.86$; when $x = 10.4$, $y = 86.62$