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) predict y when x = - 3.8 and 7.6. decide if these calculations involve interpolation or extrapolation.
(a) the slope - intercept form of the line that passes through these data points is y = &square x+&square (simplify your answers. use integers or decimals for any numbers in the equation.)

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points, say $(x_1 = 6,y_1=84.2)$ and $(x_2 = 19,y_2 = 38.7)$. Then $m=\frac{38.7 - 84.2}{19 - 6}=\frac{- 45.5}{13}=-3.5$.

Step2: Use the point - slope form to find the y - intercept

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(6,84.2)$ and $m=-3.5$, we have $y-84.2=-3.5(x - 6)$. Expand the right - hand side: $y-84.2=-3.5x+21$. Then $y=-3.5x + 105.2$. So the y - intercept $b = 105.2$.

Step3: Predict y when x=-3.8

Substitute $x=-3.8$ into the equation $y=-3.5x + 105.2$. Then $y=-3.5\times(-3.8)+105.2=13.3 + 105.2=118.5$.

Answer:

(a) $y=-3.5x + 105.2$
(b) $118.5$