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

Guida di studio - Domande di pratica

Study guide - Flashcard