Q: A pharmaceutical company tracks the concentration of a drug in a patient's bloodstream over time. If the concentration at 2 hours is 8 mg/L and at 5 hours is 2 mg/L, what is the average rate of change of the drug concentration between these times?

$\frac{8-2}{5-2} = 2\ \text{mg/L per hour}$

Q: A biologist measures the population of bacteria at two times: 1000 at hour 0 and 2500 at hour 4. What is the average rate of change of the population?

$\frac{2500-1000}{4-0} = 375\ \text{bacteria per hour}$

Q: A chemical reaction is monitored, and the temperature rises from $20^ ext{\circ}$C to $80^ ext{\circ}$C in 10 minutes. What is the average rate of change of temperature?

$\frac{80-20}{10} = 6\ ^\circ\text{C per minute}$

Question 1

A pharmaceutical company tracks the concentration of a drug in a patient's bloodstream over time. If the concentration at 2 hours is 8 mg/L and at 5 hours is 2 mg/L, what is the average rate of change of the drug concentration between these times?

Accepted Answer

$\frac{8-2}{5-2} = 2\ 	ext{mg/L per hour}$

Question 2

Which of the following equations represents the point-slope form for a line passing through $(3, -2)$ with a slope of $4$?

Accepted Answer

$y + 2 = 4(x - 3)$

Question 3

A city plans to build two roads. If the first road has a slope of $\frac{1}{2}$, what must be the slope of the second road for the roads to be perpendicular?

Accepted Answer

$-2$

Question 4

Given the function $f(x) = 3x + 7$, what is the average rate of change from $x = 1$ to $x = 4$?

Accepted Answer

$3$

Question 5

A line passes through the point $(0, 5)$ and has a slope of $-3$. Which equation represents this line in slope-intercept form?

Accepted Answer

$y = -3x + 5$

Question 6

Two lines are parallel. If the first line has the equation $y = 2x + 1$, which of the following could be the equation of the second line?

Accepted Answer

$y = 2x - 4$

Question 7

A system of equations is given by $y = 2x + 3$ and $y = -x + 1$. What is the solution to the system?

Accepted Answer

$(x, y) = (-2, -1)$

Question 8

A biologist measures the population of bacteria at two times: 1000 at hour 0 and 2500 at hour 4. What is the average rate of change of the population?

Accepted Answer

$\frac{2500-1000}{4-0} = 375\ 	ext{bacteria per hour}$

Question 9

Which of the following statements is TRUE about the slopes of perpendicular lines?

Accepted Answer

Their slopes are negative reciprocals of each other.

Question 10

A line has the equation $y = 5x - 2$. What is the y-intercept of this line?

Accepted Answer

$-2$

Question 11

A system of equations models the intersection of two streets. If the equations are $y = 3x + 2$ and $y = -x + 6$, what is the intersection point?

Accepted Answer

$(x, y) = (1, 5)$

Question 12

A line passes through $(2, 4)$ and has a slope of $-1$. Which equation represents this line in point-slope form?

Accepted Answer

$y - 4 = -1(x - 2)$

Question 13

If a line has the equation $y = -\frac{1}{3}x + 7$, what is the slope of a line perpendicular to it?

Accepted Answer

$3$

Question 14

A system of equations is given by $y = x + 2$ and $y = 4x - 1$. What is the solution to the system?

Accepted Answer

$(x, y) = (1, 3)$

Question 15

A line has a slope of $0$ and passes through $(5, 7)$. Which equation represents this line?

Accepted Answer

$y = 7$

Question 16

A chemical reaction is monitored, and the temperature rises from $20^	ext{\circ}$C to $80^	ext{\circ}$C in 10 minutes. What is the average rate of change of temperature?

Accepted Answer

$\frac{80-20}{10} = 6\ ^\circ	ext{C per minute}$

Key Concepts in Linear Equations and Systems for College Algebra

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