Question 1

Rewrite the equation $$12x - 3y - 6 = 0 in $$slope-intercept form.

Accepted Answer

$$y = 4x - 2$$

Question 2

What is the slope and y-intercept of the line $$y = 4x - 2$$?

Accepted Answer

Slope: $$4$$, y-intercept: $$-2$$

Question 3

A company’s profit $$y (in $$thousands of dollars) is modeled by $$y = 4x - 2$$, where $$x is $$the number of products sold (in thousands). What is the profit if 3,000 products are sold?

Accepted Answer

$$y = 4(3) - 2 = 10$$ thousand dollars

Question 4

Which of the following points lies on the line $$y = 4x - 2$$?

Accepted Answer

$$(1, 2)$$

Question 5

If the equation $$y = 4x - 2$$ models the cost to produce $$x$$ units, what does the slope represent in this context?

Accepted Answer

The increase in cost for each additional unit produced

Question 6

A line passes through the point $$(0, -2)$$ and has a slope of $$4. $$What is its equation in slope-intercept form?

Accepted Answer

$$y = 4x - 2$$

Question 7

Which of the following best describes the graph of $$y = 4x - 2$$?

Accepted Answer

A line that rises steeply to the right and crosses the y-axis at $$-2$$

Question 8

If the equation $$y = 4x - 2$$ represents the temperature $$y (in$$ °C) as a function of time $$x (in $$hours), what is the temperature after 0.5 hours?

Accepted Answer

$$y = 4(0.5) - 2 = 0$$ °C

Question 9

A line has the equation $$y = mx + b. If$$ $$m = 4$$ and $$b = -2$$, what is the x-intercept of the line?

Accepted Answer

$$x = 0.5$$

Question 10

Which of the following equations is parallel to $$y = 4x - 2$$?

Accepted Answer

$$y = 4x + 5$$

Question 11

If the line $$y = 4x - 2$$ models the cost of a taxi ride where $$x is $$the number of miles, what does the $$-2$$ represent?

Accepted Answer

The initial fee before any miles are traveled

Question 12

Which of the following is the correct rearrangement of $$12x - 3y - 6 = 0 to $$solve for $$y$$?

Accepted Answer

$$y = 4x - 2$$

Question 13

A line passes through $$(2, 6)$$ and has a slope of $$4. $$What is its equation?

Accepted Answer

$$y = 4x - 2$$

Question 14

If the equation $$y = 4x - 2$$ models the height $$y (in $$meters) of a plant after $$x$$ weeks, what is the height after 5 weeks?

Accepted Answer

$$y = 4(5) - 2 = 18$$ meters

Question 15

Which of the following lines is perpendicular to $$y = 4x - 2$$?

Accepted Answer

$$y = -\frac{1}{4}x + 3$$

Question 16

If the equation $$y = 4x - 2$$ represents the cost of $$x$$ pounds of apples, and you have $$y = 10$$, how many pounds did you buy?

Accepted Answer

$$x = 3$$

Question 17

What is the value of $$y$$ when $$x = -1$$ for the equation $$y = 4x - 2$$?

Accepted Answer

$$y = -6$$

Question 18

If the equation $$y = 4x - 2$$ models the number of bacteria in a culture after $$x$$ hours, and the initial number of bacteria is negative, what does this suggest about the model?

Accepted Answer

The model may not be appropriate for this real-world scenario

Question 19

A student claims the slope of the line $$y = 4x - 2 is$$ $$-2. $$What error did the student make?

Accepted Answer

They confused the y-intercept with the slope

Linear Equations: Slope-Intercept Form and Graphing

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