Annual federal spending on Medicare increased more or less linearly from $45 billion in 1973 to $87 billion in 1994. Use these data to express s, the annual spending on Medicare (in billions of dollars), as a linear function of t, the number of years since 1973.
A) $s = 2 t + 42$
B) $s = 87 t + 45$
C) $s = 2 t + 87$
D) $s = 45 t + 2$
E) $s = 2 t + 45$

Question

Annual federal spending on Medicare increased more or less linearly from $45 billion in 1973 to $87 billion in 1994. Use these data to express s, the annual spending on Medicare (in billions of dollars), as a linear function of t, the number of years since 1973. 
A) $s = 2 t + 42$
B)  $s = 87 t + 45$
C)  $s = 2 t + 87$
D)  $s = 45 t + 2$
E)  $s = 2 t + 45$

Quizplus · Accepted Answer

To find the linear function, we first calculate the slope (m) using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $y_2 = 87$, $y_1 = 45$, $x_2 = 1994 - 1973 = 21$, and $x_1 = 0$. This gives $m = \frac{87 - 45}{21} = 2$. The equation of the line is $s = mt + b$, where $b$ is the y-intercept, which is the spending in 1973, or $45 billion. Thus, the equation is $s = 2t + 45$.

Annual Federal Spending on Medicare Increased More or Less Linearly s=2t+42s = 2 t + 42s=2t+42

Annual Federal Spending on Medicare Increased More or Less Linearly $s = 2 t + 42$