Question 1

Given the points $$(-5, -7)$$ and $$(-5, -9)$$, what is the slope of the line passing through them?

A real-world example: Imagine a vertical elevator shaft where the elevator moves between two floors at $$x = -5. $$What is the slope of the path traced by the elevator?

Accepted Answer

The slope is $$\frac{-9 - (-7)}{-5 - (-5)} = \frac{-2}{0}$$, which is undefined.

Question 2

If a line passes through the points $$(2, 3)$$ and $$(2, 8)$$, what can you conclude about its slope?

Consider a flagpole standing at $$x = 2$$ with two points marked at different heights.

Accepted Answer

The slope is undefined because the $$x-$$coordinates are the same.

Question 3

A line passes through the points $$(4, 6)$$ and $$(7, 6). $$What is the slope of this line?

Imagine a road that runs horizontally from $$x = 4 to$$ $$x = 7 at a $$constant elevation of $$y = 6.$$

Accepted Answer

The slope is $$0$$ because the $$y-$$coordinates are the same.

Question 4

Given the points $$(1, 2)$$ and $$(3, 8)$$, what is the slope of the line passing through them?

A real-world example: A ramp rises from $$(1, 2) to$$ $$(3, 8). $$What is the slope of the ramp?

Accepted Answer

The slope is $$\frac{8 - 2}{3 - 1} = \frac{6}{2} = 3$$

Question 5

A line passes through the points $$(0, 0)$$ and $$(5, 10). $$What is the slope of the line?

Imagine a straight road starting at the origin and ending at $$(5, 10). $$What is the slope?

Accepted Answer

The slope is $$\frac{10 - 0}{5 - 0} = \frac{10}{5} = 2$$

Question 6

If a line passes through the points $$(7, 3)$$ and $$(7, -4)$$, what is the slope of the line?

Think of a vertical ladder at $$x = 7$$ with two rungs at $$y = 3$$ and $$y = -4.$$

Accepted Answer

The slope is undefined because the $$x-$$coordinates are the same.

Question 7

A line passes through the points $$(-2, 5)$$ and $$(4, 5). $$What is the slope of the line?

Imagine a river flowing horizontally from $$x = -2 to$$ $$x = 4 at a $$constant height of $$y = 5.$$

Accepted Answer

The slope is $$0$$ because the $$y-$$coordinates are the same.

Question 8

Given the points $$(2, 7)$$ and $$(5, 1)$$, what is the slope of the line passing through them?

A real-world example: A slide descends from $$(2, 7) to$$ $$(5, 1). $$What is the slope?

Accepted Answer

The slope is $$\frac{1 - 7}{5 - 2} = \frac{-6}{3} = -2$$

Question 9

A line passes through the points $$(3, 4)$$ and $$(6, 10). $$What is the slope of the line?

Imagine a cable stretching from $$(3, 4) to$$ $$(6, 10). $$What is the slope?

Accepted Answer

The slope is $$\frac{10 - 4}{6 - 3} = \frac{6}{3} = 2$$

Question 10

If a line passes through the points $$(0, 5)$$ and $$(0, -2)$$, what is the slope of the line?

Think of a thermometer at $$x = 0$$ with readings at $$y = 5$$ and $$y = -2.$$

Accepted Answer

The slope is undefined because the $$x-$$coordinates are the same.

Finding the Slope of a Line Given Two Points

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