Question 1

Given the line $$2x + 3y = 6$$, what is the slope of any line parallel to it?

Accepted Answer

$$-\frac{2}{3}$$

Question 2

What is the equation, in slope-intercept form, of the line passing through the point $$(-3,6)$$ and parallel to $$2x + 3y = 6$$?

Accepted Answer

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

Question 3

Which of the following is the negative reciprocal of the slope $$-\frac{2}{3}$$?

Accepted Answer

$$\frac{3}{2}$$

Question 4

Find the equation of the line passing through $$(-3,6)$$ and perpendicular to $$2x + 3y = 6 in $$slope-intercept form.

Accepted Answer

$$y = \frac{3}{2}x + \frac{21}{2}$$

Question 5

Given the data set for years and costs: $$(0, 2955), (1, 3038), (2, 3156), (3, 3242), (4, 3312), (5, 3377), (6, 3501)$$, what is the slope of the best-fit line?

Accepted Answer

$$91$$

Question 6

What is the equation of the line that models the data set above, using $$x as $$years since 2015 and $$y as $$cost?

Accepted Answer

$$y = 91x + 2955$$

Question 7

Using the equation $$y = 91x + 2955$$, what is the predicted cost for the year 2022?

Accepted Answer

$$3592$$

Question 8

If a line has the equation $$y = -\frac{2}{3}x + 2$$, what is its $$y-$$intercept?

Accepted Answer

$$2$$

Question 9

Which of the following statements is true about the lines $$y = -\frac{2}{3}x + 2$$ and $$y = -\frac{2}{3}x + 4$$?

Accepted Answer

They are parallel but have different $$y-$$intercepts.

Question 10

A real-world scenario: The cost of a college increases by a constant amount each year. If the cost in 2015 was $$2955$$ and increases by $$91$$ each year, what will the cost be in 2025?

Accepted Answer

$$3865$$

Question 11

Given the equation $$y = mx + b$$, what does the parameter $$m$$ represent in the context of a linear model for college tuition over time?

Accepted Answer

The rate of change of tuition per year.

Question 12

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

Accepted Answer

$$m_1$$ \cdot $$m_2 = -1$

Question 13

Which equation is in point-slope form for a line passing through $$(x_1$, y_1$)$$ with slope $$m$$?

Accepted Answer

$$y - y_1$ = m(x - x_1$)$$

Question 14

A line passes through $$(2, 8)$$ and has a slope of $$-4. $$What is its equation in slope-intercept form?

Accepted Answer

$$y = -4x + 16$$

Question 15

If the equation of a line is $$y = 91x + 2955$$, what does $$2955$$ represent in the context of the college cost data?

Accepted Answer

The cost in the base year (2015).

Question 16

Given the equation $$2x + 3y = 6$$, what is the $$y-$$intercept of the line?

Accepted Answer

$$2$$

Question 17

A student claims that the line $$y = -\frac{2}{3}x + 2 is $$perpendicular to $$y = \frac{3}{2}x + 1. Is $$this correct?

Accepted Answer

Yes, because their slopes are negative reciprocals.

Question 18

If a line has a slope of $$0$$, what can you say about the line?

Accepted Answer

It is horizontal.

Question 19

Suppose the cost of a product increases linearly over time. If the cost was $$100 in 2010 $$and $$160 in 2016$$, what is the annual rate of increase?

Accepted Answer

$$10$$

Question 20

Which of the following best describes the relationship between the variables in a linear model?

Accepted Answer

A constant rate of change between the variables.

Linear Equations, Parallel and Perpendicular Lines, and Linear Modeling 2.3

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