Question 1

Given the points $$A(-12, -13)$$ and $$B(18, 27)$$, what is the midpoint of the segment connecting $$A$$ and $$B$$?

Accepted Answer

$$(3, 7)$$

Question 2

What is the distance between the points $$(-12, -13)$$ and $$(18, 27)$$? Use the distance formula.

Accepted Answer

$$\sqrt{(18 + 12)^2$ + (27 + 13)^2$} = \sqrt{30^2$ + 40^2$} = \sqrt{2500} = 50$$

Question 3

Find the slope of the line passing through the points $$(-12, -13)$$ and $$(18, 27).$$

Accepted Answer

$$\dfrac{27 - (-13)}{18 - (-12)} = \dfrac{40}{30} = \dfrac{4}{3}$$

Question 4

Given the points $$(-12, -13)$$ and $$(18, 27)$$, what is the equation of the line in slope-intercept form?

Accepted Answer

$$y = \dfrac{4}{3}x - 7$$

Question 5

For the equation $$6x + 5y = 60$$, what is the $$x-$$intercept?

Accepted Answer

$$(10, 0)$$

Question 6

For the equation $$6x + 5y = 60$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, 12)$$

Question 7

What is the slope of the line $$6x + 5y = 60$$?

Accepted Answer

$$-\dfrac{6}{5}$$

Question 8

Which of the following is the correct slope-intercept form of the equation $$6x + 5y = 60$$?

Accepted Answer

$$y = -\dfrac{6}{5}x + 12$$

Question 9

A biologist is tracking the growth of a bacteria culture. The population $$P$$ after $$t$$ hours is modeled by the linear equation $$P = 150t + 200. $$What is the initial population?

Accepted Answer

$$200$$

Question 10

A car rental company charges a flat fee of $$\40$ plus $$\$$0.25$$ per mile driven. Which equation models the total cost $$C$$ for $$m$$ miles driven?

Accepted Answer

$$C = 0.25m + 40$$

Question 11

A line passes through the point $$(2, 5)$$ and has a slope of $$-3. $$What is its equation in point-slope form?

Accepted Answer

$$y - 5 = -3(x - 2)$$

Question 12

Solve the system of equations: $$\begin{cases} 3x + 4y = 48 \ 2x + 5y = 14 \end{cases}$$

Accepted Answer

$$x = 10,\ y = 4$$

Question 13

Which method is NOT a standard method for solving a system of two linear equations?

Accepted Answer

Factoring

Question 14

A line has a $$y-$$intercept of $$-7$$ and passes through the point $$(6, 5). $$What is its slope?

Accepted Answer

$$2$$

Question 15

A city taxi charges $$\3$ for the first mile and $$\$$2$$ for each additional mile. Which equation models the total fare $$F$$ for $$m$$ miles $$(m \geq 1)$$?

Accepted Answer

$$F = 2(m - 1) + 3$$

Question 16

If the equation of a line is $$y = 5x - 8$$, what is the $$x-$$intercept?

Accepted Answer

$$(1.6, 0)$$

Question 17

A student walks from point $$A(2, 3) to $$point $$B(8, 15). $$What is the length of the path walked?

Accepted Answer

$$\sqrt{(8-2)^2$ + (15-3)^2$} = \sqrt{36 + 144} = \sqrt{180} \approx 13.42$$

Question 18

Which of the following is the correct formula for the midpoint between points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$\left( \dfrac{x_1$ + x_2$}{2}, \dfrac{y_1$ + y_2$}{2} \right)$$

Question 19

Which of the following is the correct formula for the distance between points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

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

Question 20

Which of the following is the correct formula for the slope of a line passing through $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

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

College Algebra Review: Linear Functions, Formulas, and Systems

Guida di studio - Domande di pratica

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