Question 1

Which of the following equations represents a linear function whose graph is a horizontal line?

Accepted Answer

$$f(x) = -3$$

Question 2

A 100-gallon tank is being drained at a rate of 5 gallons per minute. Which of the following equations models the number of gallons, $$f(x)$$, left in the tank after $$x$$ minutes?

Accepted Answer

$$f(x) = -5x + 100$$

Question 3

Given the linear function $$f(x) = -2x + 5$$, what is the $$x-$$intercept of its graph?

Accepted Answer

$$(2.5, 0)$$

Question 4

What is the slope of the line passing through the points $$(2, -1)$$ and $$(-5, 3)$$?

Accepted Answer

$$-\frac{4}{7}$$

Question 5

If a line has the equation $$y = mx + b$$ and $$m \u003c 0$$, which of the following best describes its graph?

Accepted Answer

The line falls from left to right.

Question 6

A vertical line passes through the point $$(4, 0). $$What is its equation?

Accepted Answer

$$x = 4$$

Question 7

In 2006, online sales on Thanksgiving Day were $$205 million, and in 2011 they were 480 $$million. What is the average rate of change in sales per year?

Accepted Answer

$$55$$ million per year

Question 8

Which of the following is the slope-intercept form of a line?

Accepted Answer

$$y = mx + b$$

Question 9

A function $$f$$ has a zero at $$x = -3. $$What does this mean about the graph of $$f$$?

Accepted Answer

The graph passes through $$(-3, 0).$$

Question 10

If $$f(x) = -0.75x + 12.5$$, what is the $$y-$$intercept of the graph?

Accepted Answer

$$(0, 12.5)$$

Question 11

A line passes through $$(0, -1)$$ and has a slope of $$-\frac{1}{3}. $$What is its equation in slope-intercept form?

Accepted Answer

$$y = -\frac{1}{3}x - 1$$

Question 12

Which of the following best describes the graph of $$f(x) = b$$ where $$b 
eq 0$$?

Accepted Answer

A horizontal line with $$y-$$intercept $$b$$

Question 13

In the context of a real-world scenario, what does the $$x-$$intercept of the equation $$y = -5x + 100$$ represent if $$y is $$gallons of water and $$x is $$time in minutes?

Accepted Answer

The time it takes for the tank to be empty

Question 14

If the equation $$y = 2x - 3 is $$graphed, which of the following statements is true?

Accepted Answer

The line rises from left to right and crosses the $$y-$$axis below the origin.

Question 15

Suppose the number of text messages sent in billions, $$y$$, $$x$$ years after 2006 is modeled by $$y = 407x + 60. $$How many billions of messages were sent in 2012?

Accepted Answer

$$y = 407(6) + 60 = 2502$$

Question 16

Which of the following is NOT a property of the graph of a linear function $$f(x) = ax + b$$?

Accepted Answer

Its graph can be a parabola.

Question 17

Given the points $$(2006, 205)$$ and $$(2011, 480)$$ representing online sales in millions, what is the equation of the line modeling sales $$y in $$year $$x$$?

Accepted Answer

$$y = 55(x - 2006) + 205$$

Question 18

Which of the following best describes the meaning of the slope in the equation $$y = mx + b in a $$real-world context?

Accepted Answer

The average rate of change of $$y$$ with respect to $$x$$

Chapter 1: Linear Functions, Equations, and Inequalities – Study Notes

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