Question 1

Simplify the following expression and choose the correct answer:

$$\frac{x + 7y}{4x + 28y}$$

Accepted Answer

$$\frac{1}{4}$$

Question 2

Simplify the following expression:

$$\frac{y^2$ + 9y + 18}{y^2$ + 10y + 21}$$

Accepted Answer

$$\frac{y + 6}{y + 7}$$

Question 3

Perform the operation and simplify:

$$\frac{6x}{12x + 6} \cdot \frac{14x + 7}{3}$$

Accepted Answer

$$\frac{7x}{3}$$

Question 4

Simplify the following expression:

$$\frac{x^2$ + 15x + 54}{x^2$ + 9x + 18} \cdot \frac{x^2$ + 6x + 9}{x^2$ + 12x + 27}$$

Accepted Answer

$$1$$

Question 5

A chemist is mixing two solutions. The first solution is $$\frac{4}{y^2$ - 3y + 2}$$ and the second is $$\frac{6}{y - 1}. $$What is the sum, simplified?

Accepted Answer

$$\frac{6y - 8}{(y - 2)(y - 1)}$$

Question 6

Find the least common denominator (LCD) for the following fractions:

$$\frac{1}{4xy^3$}$$ and $$\frac{9}{6x^4$y^2$$}$

Accepted Answer

$$12x^4y^3$

Question 7

A medical researcher is analyzing the change in a patient's blood pressure over time. The blood pressure at time $$t_1 is$$ $$(9, -2)$$ and at time $$t_2 is$$ $$(-6, -1). $$What is the slope of the line passing through these points?

Accepted Answer

$$-\frac{1}{15}$$

Question 8

Find the slope and y-intercept of the line $$y = \frac{1}{10}x + \frac{4}{7}.$$

Accepted Answer

$$m = \frac{1}{10};\ (0, \frac{4}{7})$$

Question 9

Write the equation of the line in slope-intercept form that has a slope of $$\frac{5}{2}$$ and a y-intercept of $$(0, -8).$$

Accepted Answer

$$y = \frac{5}{2}x - 8$$

Question 10

A biologist is tracking the population of a species over time. The population at year 5 is $$-17$$ and at year 8 is $$-29. $$Write the equation of the line passing through the points $$(5, -17)$$ and $$(8, -29).$$

Accepted Answer

$$y = -4x + 3$$

Question 11

Which of the following graphs shows the point $$(-2, -6)$$?

Accepted Answer

![Graph 2](https://i.imgur.com/3.png)

Question 12

Find the missing coordinate to complete the ordered pair for the equation $$2x + y = -12 if$$ $$y = 4.$$

Accepted Answer

$$(-8, 4)$$

Question 13

A company’s profit can be modeled by the equation $$y = -\frac{2}{5}x. $$What is the slope of a line parallel to this profit line?

Accepted Answer

$$-\frac{2}{5}$$

Question 14

A road has a slope of $$-\frac{4}{3}. $$What is the slope of a road perpendicular to it?

Accepted Answer

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

Question 15

Find the equation of the line with slope $$m = -2$$ passing through the point $$(-6, -5).$$

Accepted Answer

$$y = -2x - 17$$

Question 16

A line passes through $$(0, 4)$$ and has a slope of $$\frac{2}{3}. $$What is its equation?

Accepted Answer

$$y = \frac{2}{3}x + 4$$

Question 17

Simplify the following expression:

$$\frac{xy(8a + 5b)}{ab(y - x)}$$

Accepted Answer

$$\frac{xy(8a + 5b)}{ab(y - x)}$$

Question 18

A horizontal line passes through the point $$(0, -6). $$What is its equation and slope?

Accepted Answer

$$m = 0;\ (0, -6)$$

Plotting Points on the Coordinate Plane

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