Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 770. Find a linear function S(t), which fits this data,
And which expresses score as a function of time.
A) $S ( t ) = - 3.75 t + 507.5$
B) $S ( t ) = 3.75 \mathrm { t } + 507.5$
C) $S ( t ) = 3.375 \mathrm { t } - 511.5$
D) $S ( t ) = 3.375 t + 511.5$

Question

Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 770. Find a linear function S(t), which fits this data,
And which expresses score as a function of time. 
A) $S ( t ) = - 3.75 t + 507.5$
B) $S ( t ) = 3.75 \mathrm { t } + 507.5$
C) $S ( t ) = 3.375 \mathrm { t } - 511.5$
D) $S ( t ) = 3.375 t + 511.5$

Quizplus · Accepted Answer

To find the correct linear function, we can use the two given points: (30, 620) and (70, 770). The slope $m$ of the line is calculated as $\frac{770 - 620}{70 - 30} = \frac{150}{40} = 3.75$. To find the y-intercept $b$, we can use one of the points and the slope in the equation $y = mx + b$. Using the point (30, 620), we get $620 = 3.75(30) + b$, solving for $b$ gives $b = 620 - 112.5 = 507.5$. Therefore, the linear function is $S(t) = 3.75t + 507.5$.

Persons Taking a 30-Hour Review Course to Prepare for a Standardized