Question 1

Which of the following best describes the rectangular coordinate system?

Accepted Answer

It is formed by two number lines intersecting at a right angle, called the x-axis and y-axis.

Question 2

Given the points $$(2, 5)$$ and $$(8, 11)$$, what is the midpoint between them?

Accepted Answer

$$(5, 8)$$

Question 3

A city park is represented on a map with the southwest corner at $$(1, 3)$$ and the northeast corner at $$(7, 9). $$What is the distance, in map units, between these two corners?

Accepted Answer

$$\sqrt{(7-1)^2$ + (9-3)^2$} = \sqrt{36 + 36} = \sqrt{72} = 6\sqrt{2}$$

Question 4

If a line passes through the points $$(-2, 4)$$ and $$(3, -1)$$, what is its slope?

Accepted Answer

$$\frac{-1 - 4}{3 - (-2)} = \frac{-5}{5} = -1$$

Question 5

A hiking trail starts at $$(0, 0)$$ and ends at $$(6, 8). $$Using the Pythagorean Theorem, what is the length of the trail?

Accepted Answer

$$\sqrt{6^2$ + 8^2$} = \sqrt{36 + 64} = \sqrt{100} = 10$$

Question 6

A company’s revenue increased from $$\50$$,000$$ in 2015 to $$\$$80,000 in 2020. $$What is the average annual rate of increase?

Accepted Answer

$$\frac{80,000 - 50,000}{2020 - 2015} = \frac{30,000}{5} = 6,000$$

Question 7

Which of the following lines is horizontal?

Accepted Answer

A line with slope $$m = 0$$

Question 8

A vertical line passes through the point $$(4, 7). $$Which of the following is true about its slope?

Accepted Answer

The slope is undefined.

Question 9

A student records the following data: In 2010, a bus ticket cost $$\1.25$; in 2020, it cost $$\$$2.00. $$What is the annual rate of increase in the ticket price?

Accepted Answer

$$\frac{2.00 - 1.25}{2020 - 2010} = \frac{0.75}{10} = 0.075$$

Question 10

If the points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$ are $$(5, -2)$$ and $$(-3, 6)$$, what is the midpoint?

Accepted Answer

$$\left( \frac{5 + (-3)}{2}, \frac{-2 + 6}{2} \right) = (1, 2)$$

Question 11

A new laptop with 128GB storage costs $$\640$, and a 256GB model costs $$\$$880. $$What is the cost rate per gigabyte between these two models?

Accepted Answer

$$\frac{880 - 640}{256 - 128} = \frac{240}{128} = 1.875$$

Question 12

Which of the following statements is true about the slope of a line?

Accepted Answer

If $$m \u003e 0$$, the line is increasing.

Question 13

Given the points $$(7, 2)$$ and $$(7, -5)$$, what is the slope of the line passing through them?

Accepted Answer

The slope is undefined.

Question 14

A road rises 12 meters for every 100 meters of horizontal distance. What is the slope of the road?

Accepted Answer

$$\frac{12}{100} = 0.12$$

Question 15

If a line has a slope of $$-\frac{3}{4}$$, which of the following best describes its direction?

Accepted Answer

The line is decreasing.

Question 16

A college’s enrollment dropped from 15,000 students in 2012 to 12,000 students in 2018. What is the average annual rate of decline?

Accepted Answer

$$\frac{12,000 - 15,000}{2018 - 2012} = \frac{-3,000}{6} = -500$$

Question 17

Which formula is used to find the distance between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$d = \sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 18

A line passes through $$(0, 0)$$ and $$(4, 6). $$What is its slope?

Accepted Answer

$$\frac{6 - 0}{4 - 0} = \frac{6}{4} = 1.5$$

Question 19

Which axis is vertical in the rectangular coordinate system?

Accepted Answer

The y-axis

Rectangular Coordinates & Slope: College Algebra Study Notes

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