Question 1

Which of the following equations represents a vertical line in the rectangular coordinate system?

Accepted Answer

$$x = -2$$

Question 2

What is the $$y-$$intercept of the line given by the equation $$2x - 3y = 6$$?

Accepted Answer

$$(0, -2)$$

Question 3

Which ordered pair is a solution to the equation $$x + 2y = 7$$?

Accepted Answer

$$(3, 2)$$

Question 4

A company charges a flat fee of $$\50$ plus $$\$$20$$ per hour for consulting. Which equation models the total cost $$C$$ for $$h$$ hours of consulting?

Accepted Answer

$$C = 20h + 50$$

Question 5

Find the $$x-$$intercept of the line $$4x + 2y = 8.$$

Accepted Answer

$$(2, 0)$$

Question 6

Which of the following best describes the graph of $$y = -3$$?

Accepted Answer

A horizontal line through $$y = -3$$

Question 7

If the point $$(a, b)$$ lies on the graph of $$2x - y = 5$$, which equation must be true?

Accepted Answer

$$2a - b = 5$$

Question 8

A chemist mixes two solutions. The total volume $$V in $$liters after $$t$$ hours is given by $$V = 3t + 10. $$What is the initial volume?

Accepted Answer

$$10$$ liters

Question 9

Which of the following is the standard form of a linear equation in two variables?

Accepted Answer

$$Ax + By = C$$

Question 10

A taxi company charges $$\3$ for the first mile and $$\$$2$$ for each additional mile. Which equation gives the total cost $$C$$ for $$m$$ miles (where $$m \geq 1$$)?

Accepted Answer

$$C = 3 + 2(m-1)$$

Question 11

If the equation of a line is $$y = -x + 3$$, what is the $$y-$$coordinate when $$x = 5$$?

Accepted Answer

$$-2$$

Question 12

Which of the following points lies on the line $$3x + 2y = 12$$?

Accepted Answer

$$(2, 3)$$

Question 13

A medical researcher tracks the temperature $$T (in$$ $$^\circC) of a $$patient over time $$t (in $$hours) using $$T = 0.5t + 36. $$What does the slope represent in this context?

Accepted Answer

The rate of temperature increase per hour

Question 14

Which of the following is NOT a solution to the equation $$x - y = 4$$?

Accepted Answer

$$(2, 3)$$

Question 15

If a line passes through the points $$(0, 2)$$ and $$(4, 0)$$, what is its equation in standard form?

Accepted Answer

$$x + 2y = 4$$

Question 16

A biologist models the population $$P of a $$bacteria culture as $$P = 500 - 20t$$, where $$t is $$time in hours. What does the $$x-$$intercept represent in this context?

Accepted Answer

The time when the population reaches zero

Question 17

Which of the following statements is TRUE about the graph of $$x = 5$$?

Accepted Answer

It is a vertical line through $$x = 5$$

Question 18

Given the equation $$y = 2x - 7$$, what is the $$x-$$intercept?

Accepted Answer

$$(3.5, 0)$$

Question 19

A line passes through $$(0, 4)$$ and has a slope of $$-2. $$Which equation represents this line?

Accepted Answer

$$y = -2x + 4$$

Question 20

If the equation $$2x + y = 8$$ models the relationship between the number of hours $$x$$ spent studying and the score $$y on a $$test, what is the score when $$x = 3$$?

Accepted Answer

Graphing Linear Equations in Two Variables and the Rectangular Coordinate System

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