Question 1

Given the equation $$y = mx + b$$, what does the parameter $$m$$ represent in the context of a real-world scenario, such as Sonya walking away from home at a constant speed?

Accepted Answer

The rate at which Sonya is walking away from home

Question 2

Sonya is 10 miles from home and walks away at 2 miles per hour. Which equation models her distance from home $$t$$ hours from now?

Accepted Answer

$$y = 2t + 10$$

Question 3

A boat is 100 miles from the marina, sailing directly toward it at 10 miles per hour. What is the equation for its distance from the marina after $$t$$ hours?

Accepted Answer

$$y = 100 - 10t$$

Question 4

Which of the following equations represents a line with a negative slope and a $$y-$$intercept of $$-4$$?

Accepted Answer

$$f(x) = -x - 4$$

Question 5

Given the two functions $$f(x) = 5x - 1$$ and $$g(x) = 6 - x$$, at what $$x-$$value do they intersect?

Accepted Answer

$$x = 1.17$$

Question 6

What is the $$y-$$intercept of the line $$y = -2x + 2$$?

Accepted Answer

$$2$$

Question 7

Which equation matches a line that passes through the point $$(0, 1)$$ and has a slope of $$3$$?

Accepted Answer

$$y = 3x + 1$$

Question 8

If a line has the equation $$y = 3x - \frac{1}{3}$$, what is its slope?

Accepted Answer

$$3$$

Question 9

Which of the following equations represents a line parallel to $$y = 3x + 1$$?

Accepted Answer

$$y = 3x - 4$$

Question 10

Given the system of equations $$7x + 2y = -1$$ and $$21x + 6y = -3$$, what can you conclude about the system?

Accepted Answer

The system has infinitely many solutions

Question 11

Which transformation occurs when the equation $$y = x is $$changed to $$y = x + 2$$?

Accepted Answer

A vertical shift up by 2 units

Question 12

If the equation of a line is $$y = -\frac{1}{3}x$$, what is the $$y-$$intercept?

Accepted Answer

$$0$$

Question 13

Which equation represents a line with a slope of $$\frac{1}{3}$$ and a $$y-$$intercept of $$2$$?

Accepted Answer

$$f(x) = \frac{1}{3}x + 2$$

Question 14

Given the system $$-4x + y = 5$$ and $$8x - 2y = 3$$, what is the solution for $$x$$?

Accepted Answer

$$x = -1$$

Question 15

Which of the following best describes the slope of the line $$y = -2x + 2$$?

Accepted Answer

The line decreases by 2 units in $$y$$ for every 1 unit increase in $$x$$

Question 16

If two lines have the same slope but different $$y-$$intercepts, what is true about their graphs?

Accepted Answer

They are parallel and never intersect

Question 17

Which equation represents a line perpendicular to $$y = x$$?

Accepted Answer

$$y = -x$$

Question 18

A line passes through $$(0, -4)$$ and has a slope of $$-3. $$What is its equation?

Accepted Answer

$$y = -3x - 4$$

Question 19

If the equation of a line is $$y = 3x + 1$$, what is the value of $$y$$ when $$x = 2$$?

Accepted Answer

$$y = 7$$

Question 20

Which of the following equations has a slope of $$-2$$ and a $$y-$$intercept of $$2$$?

Accepted Answer

$$y = -2x + 2$$

Linear Functions, Graphs, and Systems of Equations: Precalculus Study Notes

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