Scientists have discovered that a linear relationship exists between the amount of flobberworm mucus secretions and the air temperature. When the temperature is $65 ^ { \circ } \mathrm { F }$, the flobberworms each secrete 16 grams of mucus a day; when the temperature is $95 ^ { \circ } \mathrm { F }$, they each secrete 22 grams of mucus a day. Find a function $M ( t )$ that gives the amount of mucus secreted on a given day, where $t$ is the temperature of that day in degrees Fahrenheit.
A) $M ( t ) = 0.2 t + 16$
B) $M ( t ) = 5 t + 16$
C) $M ( t ) = 5 t + 3$
D) $M ( t ) = 0.2 t + 3$

Question

Quizplus · Accepted Answer

To find the function $M(t)$, we first determine the slope of the line connecting the two given points $(65, 16)$ and $(95, 22)$. The slope $m$ is given by $\frac{22 - 16}{95 - 65} = \frac{6}{30} = 0.2$. Then, using the point-slope form of a line, $y - y_1 = m(x - x_1)$, and substituting one of the points (e.g., $65, 16$), we solve for $y$ (or $M(t)$ in this case) to find the equation of the line. Substituting $m = 0.2$, $x_1 = 65$, and $y_1 = 16$, we get $M(t) - 16 = 0.2(t - 65)$. Simplifying, $M(t) = 0.2t - 0.2 \cdot 65 + 16$, which simplifies further to $M(t) = 0.2t + 3$.

Scientists Have Discovered That a Linear Relationship Exists Between the Amount