Question 1

Which of the following points lies in Quadrant III of the rectangular coordinate system?

Accepted Answer

$$(-3, -2)$$

Question 2

Given the equation $$x + y = 7$$, which of the following points satisfies the equation?

Accepted Answer

$$(3, 4)$$

Question 3

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

Accepted Answer

$$(0, -3)$$

Question 4

A biologist is tracking the growth of a plant, which can be modeled by the equation $$y = 2x + 5$$, where $$y is $$the height in cm after $$x$$ weeks. What is the slope of the line, and what does it represent in this context?

Accepted Answer

Slope is $$2$$; the plant grows $$2 cm $$per week.

Question 5

Find the slope of the line passing through the points $$(1, 2)$$ and $$(4, 8).$$

Accepted Answer

$$2$$

Question 6

Which of the following equations represents a vertical line?

Accepted Answer

$$x = -2$$

Question 7

A company’s profit $$P (in $$thousands of dollars) after $$x$$ months is modeled by $$P = -4x + 20. $$What is the $$x-$$intercept, and what does it represent?

Accepted Answer

$$x = 5$$; the company breaks even after 5 months.

Question 8

Given the equation $$y = \sqrt{x + 1}$$, which of the following points is on the graph?

Accepted Answer

$$(0, 1)$$

Question 9

What is the equation of the line in point-slope form that passes through $$(2, -1)$$ with a slope of $$3$$?

Accepted Answer

$$y + 1 = 3(x - 2)$$

Question 10

A road rises $$8$$ meters for every $$200$$ meters of horizontal distance. What is the slope of the road?

Accepted Answer

$$\frac{8}{200}$$

Question 11

Which of the following lines is parallel to $$y = -\frac{1}{2}x + 4$$?

Accepted Answer

$$y = -\frac{1}{2}x - 3$$

Question 12

Find the equation of the line in slope-intercept form that passes through $$(0, 5)$$ and $$(2, 1).$$

Accepted Answer

$$y = -2x + 5$$

Question 13

Which of the following statements about the slopes of perpendicular lines is true?

Accepted Answer

Their slopes are negative reciprocals of each other.

Question 14

Given the standard form equation $$4x - 2y = 8$$, what is the slope of the line?

Accepted Answer

$$-2$$

Question 15

A horizontal line passes through the point $$(3, -2). $$What is its equation?

Accepted Answer

$$y = -2$$

Question 16

If a line has the equation $$y = 5$$, what is its slope?

Accepted Answer

$$0$$

Question 17

Find the $$x- $$and $$y-$$intercepts of the equation $$2x + 3y = 12.$$

Accepted Answer

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

Question 18

Which of the following is the correct slope-intercept form of the line perpendicular to $$y = 2x - 1$$ and passing through $$(0, 3)$$?

Accepted Answer

$$y = -\frac{1}{2}x + 3$$

Question 19

A line passes through the points $$(-1, 4)$$ and $$(3, -8). $$What is its slope?

Accepted Answer

$$-3$$

Question 20

Which of the following best describes the relationship between the lines $$y = 3x + 2$$ and $$y = 3x - 4$$?

Accepted Answer

They are parallel.

Graphs of Equations: The Rectangular Coordinate System and Lines

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