Question 1

Given the points $$(-3, 2)$$ and $$(2, -4)$$, what is the equation of the line passing through these points in standard form $$Ax + By = C$$?

Accepted Answer

$$6x + 5y = -8$$

Question 2

A line passes through the point $$(3, 5)$$ and is parallel to the line $$2x + 5y = 4. $$What is the equation of this line in slope-intercept form?

Accepted Answer

$$y = -\frac{2}{5}x + \frac{31}{5}$$

Question 3

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

Accepted Answer

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

Question 4

If a line has a slope of $$-3$$ and passes through the point $$(-4, 1)$$, what is its equation in slope-intercept form?

Accepted Answer

$$y = -3x - 11$$

Question 5

Which of the following statements is TRUE about the slopes of two perpendicular lines (neither vertical)?

Accepted Answer

Their slopes are negative reciprocals of each other.

Question 6

A vertical line passes through the point $$(a, b). $$What is its equation?

Accepted Answer

$$x = a$$

Question 7

Given the equation $$4x + 5y = -10$$, what is the slope and $$y-$$intercept of the line?

Accepted Answer

Slope: $$-\frac{4}{5}$$, $$y-$$intercept: $$(0, -2)$$

Question 8

A line passes through $$(1, 1)$$ and $$(2, 4). $$What is its equation in slope-intercept form?

Accepted Answer

$$y = 3x - 2$$

Question 9

Which of the following best describes the equation of a horizontal line passing through $$(a, b)$$?

Accepted Answer

$$y = b$$

Question 10

If the average tuition at a public college increases by $$236 per year$$ and was $$8070 in 2013$$, what is the equation modeling the tuition $$y as a $$function of years $$x$$ since 2013?

Accepted Answer

$$y = 236x + 8070$$

Question 11

A line is perpendicular to $$2x + 5y = 4$$ and passes through $$(3, 5). $$What is its equation in standard form?

Accepted Answer

$$5x - 2y = 5$$

Question 12

Which of the following is the correct definition of the slope $$m$$ between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

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

Question 13

If a line has the equation $$y = mx + b$$, what is the $$y-$$intercept of the line?

Accepted Answer

$$(0, b)$$

Question 14

A real estate agent models the price $$y (in $$thousands of dollars) of a house as a function of its size $$x (in $$hundreds of square feet) by the equation $$y = 50x + 100. $$What is the predicted price of a $$2,000$$ square foot house?

Accepted Answer

$$y = 200$$ thousand dollars

Question 15

Which of the following is NOT a characteristic of the standard form $$Ax + By = C$$ for a line?

Accepted Answer

The slope is always $$A$$

Question 16

A graphing calculator is used to solve $$-4(2-x) = 3x + 4. $$What is the solution for $$x$$?

Accepted Answer

$$x = -12$$

Question 17

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

Accepted Answer

They have the same slope.

Question 18

A line has the equation $$y = 0. $$Which of the following statements is true?

Accepted Answer

It is a horizontal line passing through the $$x-$$axis.

Question 19

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P = 5x - 20$$, where $$x is $$the number of units sold (in hundreds). How many units must be sold for the company to break even?

Accepted Answer

$$x = 4$$

Equations of Lines and Linear Models: Forms, Properties, and Applications

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