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. the slope - intercept form of the line that passes through these data points is y = - 3.5x + 105.2 (a) simplify your answers. use integers or decimals for any numbers in the equation. (b) predict y when x = - 3.8. simplify your answer. round to the nearest hundredth. y = 118.5 predict y for the following values of x. is an example of which of the following? interpolation extrapolation

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. We are given $y=-3.5x + 105.2$.

Step2: Find y when x = - 3.8

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

Step3: Predict y for given x

We are asked to predict $y$ for a value of $x$. Since we have the equation $y=-3.5x + 105.2$, we can use it for interpolation or extrapolation.

Answer:

(a) The slope of the line is $m=-3.5$ and the y - intercept is $b = 105.2$.
(b) When $x=-3.8$, $y = 118.5$.