Question 1

Is the point $$(4, -1) a $$solution to the equation $$4x - 7y = 9$$? How many solutions does this equation have?

Accepted Answer

No; the equation has infinitely many solutions.

Question 2

What does the graph of a linear equation in two variables represent?

Accepted Answer

A straight line showing all possible solutions

Question 3

Find the $$x- $$and $$y-$$intercepts of the equation $$3x + 5y = 6.$$

Accepted Answer

$$x-$$intercept: $$(2, 0)$$; $$y-$$intercept: $$(0, 1.2)$$

Question 4

Given the lines $$10x + 6y = 0$$ and $$3y = -5x + 7$$, are the lines parallel, perpendicular, or neither?

Accepted Answer

Parallel

Question 5

Write the equation of the line passing through $$(4, -5)$$ and $$(-6, 2) in $$slope-intercept form.

Accepted Answer

$$y = -\frac{7}{10}x - \frac{11}{5}$$

Question 6

A line passes through $$(2, -3)$$ and is parallel to $$y = \frac{2}{3}x - 4. $$What is its equation in standard form?

Accepted Answer

$$2x - 3y = 13$$

Question 7

Justin's fixed cost for baking cakes is $$1500, and each cake costs 7$ in materials. What is the linear equation for his total cost C$ for x$ cakes, and what is the cost for 45$ cakes?

Accepted Answer

$$C = 7x + 1500$$; $$C = 1815$$ for $$45$$ cakes

Question 8

In 2009, Missouri's minimum wage was $$7.05. In 2019, it was 8.60. $$What is the average rate of change per year, rounded to the nearest cent?

Accepted Answer

$$0.16$$ per year

Question 9

Find the midpoint of the segment with endpoints $$P(-4, 7)$$ and $$Q(2, -1).$$

Accepted Answer

$$(-1, 3)$$

Question 10

Solve the system: $$x - 4y = -13$$, $$y = -2x - 3. $$What is the solution?

Accepted Answer

$$(-5, 2)$$

Question 11

A train travels $$400$$ miles in the same time a truck travels $$325$$ miles. The train's speed is $$15$$ mph faster than the truck's. What are their speeds?

Accepted Answer

Train: $$80$$ mph, Truck: $$65$$ mph

Question 12

Find the intersection: $$\{0,2,4,6\} \cap \{0,3,6,8\}$$

Accepted Answer

$$\{0, 6\}$$

Question 13

Solve the compound inequality: $$x + 4 \u003e 12$$ and $$x - 2 \u003c 12. $$Give the solution in interval notation.

Accepted Answer

$$[8, 14)$$

Question 14

Solve: $$|x| = 3$$

Accepted Answer

$$x = 3 or$$ $$x = -3$$

Question 15

Solve: $$|x| = -10$$

Accepted Answer

No solution

Question 16

Solve: $$|3x - 7| = 8$$

Accepted Answer

$$x = 5 or$$ $$x = -\frac{1}{3}$$

Question 17

Solve the inequality: $$|-x + 6| \leq 4. $$Give the solution in interval notation.

Accepted Answer

$$[2, 10]$$

Question 18

Find the union: $$\{0,2,4,6\} \cup \{0,3,6,8\}$$

Accepted Answer

$$\{0, 2, 3, 4, 6, 8\}$$

Question 19

Solve: $$|9x - 2| + 4 = 7$$

Accepted Answer

$$x = \frac{5}{9} or$$ $$x = -\frac{1}{9}$$

Step-by-Step Guidance for Intermediate Algebra Practice Exam (Ch 7, 8)

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