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 = - 3.8 and 7.6. (b) the slope - intercept form of the line that passes through these data points is y = - 3.5x + 105.2. use integers or decimals for any numbers in the equation. (simplify your answers.) predict y when x = - 3.8. (simplify your answer. round to the nearest hundredth.) y = 118.5 predict y for this value of x is an example of which of the following? interpolation extrapolation predict y when x = 7.6. (simplify your answer. round to the nearest hundredth.)

Explanation:

Step1: Identify the slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m=-3.5$ and $b = 105.2$ in the given equation $y=-3.5x + 105.2$.

Step2: Predict $y$ 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 $y$ when $x = 7.6$

Substitute $x = 7.6$ into the equation $y=-3.5x + 105.2$.
$y=-3.5\times7.6+105.2$.
First, calculate $-3.5\times7.6=-26.6$.
Then, $y=-26.6+105.2 = 78.6$.

Answer:

(a) When $x=-3.8$, $y = 118.5$.
(b) When $x = 7.6$, $y=78.6$.