Interpreting Linear Models - Pre Algebra

1. In a linear model $y = mx + b$, what does $b$ represent in context?

   The initial value: the value of $y$ when $x = 0$.

2. A car's value is modeled by $V = -0.8t + 24$, in thousands of dollars, where $t$ is age in years. What does $-0.8$ mean?

   The car loses 0.8 thousand dollars (800 dollars) of value each year.

3. In the model $d = 60t$, $d$ is distance in miles and $t$ is time in hours. What are the units of the slope 60?

   Miles per hour. A slope has units of output units per input unit.

4. The model $T = -3.5h + 72$ was built from altitudes $h$ of 0 to 10 thousand feet. Which prediction is extrapolation: $h = 6$ or $h = 30$?

   $h = 30$. It lies outside the 0 to 10 range of the data; $h = 6$ lies inside it.

5. What is extrapolation when using a linear model?

   Using the model to predict values for inputs outside the range of the data used to build it.

6. Why can extrapolation give unreasonable predictions?

   The linear trend may not continue outside the data range, so the model can predict impossible values, such as negative prices.

7. A car's value is modeled by $V = -0.8t + 24$, in thousands of dollars, where $t$ is age in years. What does 24 mean?

   The model's value at age $t = 0$ is 24 thousand dollars, the starting value.

8. Subscribers are modeled by $N = 25t + 100$, in thousands, where $t$ is months since launch. What does 100 mean?

   There were 100 thousand subscribers at launch, when $t = 0$.

9. The model $V = -0.8t + 24$ (thousands of dollars) was built from cars aged 1 to 10 years. What value does it predict at $t = 40$?

   $-8$ thousand dollars, which is impossible. Age 40 is far outside the data, so this extrapolation is unreasonable.

10. In a linear model $y = mx + b$, what does $m$ represent in context?

    The rate of change: how much $y$ changes for each increase of 1 in $x$.

11. What is a prediction made inside the range of the data used to build a model called?

    Interpolation. It is generally more reliable than extrapolation.

12. A plant's height is modeled by $h = 1.5w + 4$, in centimeters, where $w$ is weeks. How much does the model say it grows each week?

    1.5 centimeters per week, the slope.

Study these flashcards