Q: A meteorologist models the relationship between atmospheric CO$$_2$$ concentration $$x (in $$ppm) and average global temperature $$f(x) (in$$ $$^ ext{o}C) $$with the linear function $$f(x) = 0.016x + 51.1. $$What is the predicted temperature when $$x = 400$$ ppm?

$$f(400) = 0.016 \times 400 + 51.1 = 57.5$$

Q: Which of the following statements is true about the general form $$Ax + By + C = 0$$?

The slope is $$-\dfrac{A}{B} if$$ $$B \neq 0.$$

Question 1

A biologist is tracking the growth of a plant. On day 2, the plant is 5 cm tall, and on day 8, it is 17 cm tall. What is the average rate of growth (slope) of the plant per day?

Accepted Answer

$$m = \dfrac{17 - 5}{8 - 2} = 2$$

Question 2

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

Accepted Answer

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

Question 3

A company’s profit $$P (in $$thousands of dollars) is modeled by the linear function $$P(x) = 4x - 10$$, where $$x is $$the number of products sold (in hundreds). What is the y-intercept and what does it represent?

Accepted Answer

y-intercept is $$-10$$; it represents the profit when no products are sold.

Question 4

Which equation represents a horizontal line passing through the point $$(0, 7)$$?

Accepted Answer

$$y = 7$$

Question 5

Given the general form of a line $$3x - 4y + 8 = 0$$, what is the slope of the line?

Accepted Answer

$$m = \dfrac{3}{-4} = -\dfrac{3}{4}$$

Question 6

A vertical line passes through the point $$(5, -2). $$Which of the following is its equation?

Accepted Answer

$$x = 5$$

Question 7

A meteorologist models the relationship between atmospheric CO$$_2$$ concentration $$x (in $$ppm) and average global temperature $$f(x) (in$$ $$^	ext{o}C) $$with the linear function $$f(x) = 0.016x + 51.1. $$What is the predicted temperature when $$x = 400$$ ppm?

Accepted Answer

$$f(400) = 0.016 	imes 400 + 51.1 = 57.5$$

Question 8

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

Accepted Answer

Undefined

Question 9

Given the equation $$2x + 3y = 12$$, what are the x- and y-intercepts?

Accepted Answer

x-intercept: $$(6, 0)$$; y-intercept: $$(0, 4)$$

Question 10

A line passes through the points $$(1, 2)$$ and $$(4, 8). $$What is its equation in slope-intercept form?

Accepted Answer

$$y = 2x ($$since the y-intercept is 0)

Question 11

A city’s water usage $$W (in $$millions of gallons) is modeled by $$W = -0.5t + 30$$, where $$t is $$the number of days since the start of a drought. What does the slope represent in this context?

Accepted Answer

Water usage decreases by 0.5 million gallons per day.

Question 12

Which of the following is the correct slope-intercept form for a line with slope $$-3$$ and y-intercept $$7$$?

Accepted Answer

$$y = -3x + 7$$

Question 13

A chemist records the temperature of a reaction at two different times: at 10 minutes, the temperature is 25°C, and at 30 minutes, it is 45°C. Write the equation of the line modeling temperature $$T as a $$function of time $$t (in $$minutes).

Accepted Answer

$$T = 1t + 15$$

Question 14

If a line has the equation $$y = 0$$, which of the following statements is true?

Accepted Answer

It is a horizontal line passing through the origin.

Question 15

Given the equation $$y - 4 = 2(x + 1)$$, what is the slope and a point on the line?

Accepted Answer

Slope is $$2$$; point is $$(-1, 4)$$

Question 16

A line passes through $$(0, -3)$$ and has a slope of $$\dfrac{5}{2}. $$What is its equation in slope-intercept form?

Accepted Answer

$$y = \dfrac{5}{2}x - 3$$

Question 17

Which of the following statements is true about the general form $$Ax + By + C = 0$$?

Accepted Answer

The slope is $$-\dfrac{A}{B} if$$ $$B 
eq 0.$$

Question 18

A student claims that the equation $$x = 4$$ represents a horizontal line. Is this correct? Why or why not?

Accepted Answer

No, because $$x = 4 is a $$vertical line.

Question 19

A car rental company charges a flat fee of $$\20$ plus $$\$$0.15$$ per mile driven. Write a linear function $$C(m)$$ for the total cost in dollars for driving $$m$$ miles, and identify the slope and y-intercept.

Accepted Answer

$$C(m) = 0.15m + 20$$; slope is $$0.15$$, y-intercept is $$20$$

Linear Functions and Graphs: Slope, Equations, and Applications

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