Question 1

What is the formula for the slope $$m of a $$line passing through two distinct points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$m = \frac{y_2$ - y_1$}{x_2$ - x_1$}$$

Question 2

Find the slope of the line passing through the points $$(4, -2)$$ and $$(-1, 5). $$What does the sign of the slope indicate about the line?

Accepted Answer

$$m = -1.4$$, the line falls from left to right.

Question 3

Which of the following best describes the slope of a horizontal line?

Accepted Answer

The slope is zero.

Question 4

Given the points $$(1, 6)$$ and $$(1, 4)$$, what is the slope of the line passing through them?

Accepted Answer

The slope is undefined.

Question 5

If two nonvertical lines are parallel, which of the following must be true?

Accepted Answer

Their slopes are equal.

Question 6

Show that the lines passing through $$(4, 2)$$ and $$(6, 6)$$, and through $$(0, -2)$$ and $$(1, 0)$$ are parallel.

Accepted Answer

Both lines have slope $$2$$, so they are parallel.

Question 7

If two nonvertical lines are perpendicular, what is true about their slopes $$m_1$$ and $$m_2$$?

Accepted Answer

$$m_1$$ $$m_2 = -1$

Question 8

A line passes through $$(-1, 4)$$ and $$(3, 2). $$Another line passes through $$(-2, -1)$$ and $$(2, 7). $$Are these lines perpendicular?

Accepted Answer

Yes, because the product of their slopes is $$-1.$$

Question 9

Which of the following statements is true about the relationship between a horizontal and a vertical line?

Accepted Answer

A horizontal line is perpendicular to a vertical line.

Question 10

The graph shows the number of American men living alone increased from $$11.2$$ million in $$2000 to$$ $$15.8$$ million in $$2016. $$What is the slope of the line segment representing this change, and what does it mean?

Accepted Answer

$$m = 0.29$$, meaning the number increased by $$0.29$$ million men per year.

Question 11

Suppose the number of U.S. women living alone increased from $$15.5$$ million in $$2000 to$$ $$19.6$$ million in $$2016. $$What is the rate of change?

Accepted Answer

$$m = \frac{19.6 - 15.5}{2016 - 2000} = 0.256$$

Question 12

Which of the following best describes the meaning of slope in a real-world context?

Accepted Answer

It represents the rate of change of one variable with respect to another.

Question 13

A road rises $$30$$ meters for every $$500$$ meters of horizontal distance. What is the slope of the road?

Accepted Answer

$$m = \frac{30}{500} = 0.06$$

Question 14

If a line has a slope of $$-\frac{3}{4}$$, what is the slope of a line perpendicular to it?

Accepted Answer

$$\frac{4}{3}$$

Question 15

Which of the following is NOT a possible value for the slope of a line?

Accepted Answer

Infinity

Question 16

A company’s profit increased from $$\10$$,000$$ in 2010$ to $$\$$25,000 in$$ $$2015. $$What is the average rate of change in profit per year?

Accepted Answer

$$m = \frac{25,000 - 10,000}{2015 - 2010} = 3,000$$

Slope and Its Applications in Linear Equations and Inequalities in Two Variables

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