Question 1

Given two points $A = (x_1, y_1)$ and $B = (x_2, y_2)$, what is the formula for the slope $m$ of the line passing through these points?

Accepted Answer

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Question 2

If a line passes through the points $(-2, 6)$ and $(4, 9)$, what is its slope?

Accepted Answer

$m = \frac{9 - 6}{4 - (-2)} = \frac{3}{6} = 0.5$

Question 3

Which of the following best describes the slope of a vertical line?

Accepted Answer

The slope is undefined because the change in $x$ is zero.

Question 4

A horizontal line is represented by which of the following equations?

Accepted Answer

$y = c$

Question 5

Given the equation $2x - 4y - 7 = 0$, what is the slope and $y$-intercept of the line?

Accepted Answer

Slope: $m = 0.5$, $y$-intercept: $b = 1.75$

Question 6

Which of the following is the slope-intercept form of a linear equation?

Accepted Answer

$y = mx + b$

Question 7

If the graph of a function $f(x)$ is a vertical line, which statement is true?

Accepted Answer

It does not represent a function.

Question 8

A business has a fixed cost of $10,000$ per month and a variable cost of $20$ per unit produced. What is the total cost function $C(x)$ for producing $x$ units?

Accepted Answer

$C(x) = 20x + 10,000$

Question 9

Given the point $(3, -6)$ and a slope $m = 4$, what is the equation of the line in point-slope form?

Accepted Answer

$y + 6 = 4(x - 3)$

Question 10

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

Accepted Answer

They are parallel.

Question 11

The average rate of change of the amount spent on cancer research from year 2000 to 2010 is calculated using which formula?

Accepted Answer

$\frac{f(2010) - f(2000)}{2010 - 2000}$

Question 12

Which of the following is the point-slope form of a line passing through $(x_1, y_1)$ with slope $m$?

Accepted Answer

$y - y_1 = m(x - x_1)$

Question 13

A company sells a product at a unit price of $50$ and sells $x$ units. What is the total revenue function $R(x)$?

Accepted Answer

$R(x) = 50x$

Question 14

If the cost function is $C(x) = 20x + 10,000$ and the revenue function is $R(x) = 50x$, at what quantity $x$ does the break-even point occur?

Accepted Answer

$x = 333.33$

Question 15

Which of the following statements is true about the graph of $y = mx$?

Accepted Answer

It passes through the origin and has slope $m$.

Question 16

If a line has equation $y = -3x + 7$, what is its $y$-intercept?

Accepted Answer

$b = 7$

Question 17

Which of the following is NOT a property of linear functions?

Accepted Answer

They have a variable rate of change.

Question 18

A line passes through $(1, 2)$ and has slope $m = -5$. What is its equation in slope-intercept form?

Accepted Answer

$y = -5x + 7$

Question 19

If the equation of a line is $y = mx + b$, what does the constant $b$ represent?

Accepted Answer

The $y$-intercept of the line.

Fundamentals of Linear Functions and Slope in Calculus

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