A linear relationship between the quantities x and y is represented in

Praxis 5003 Practice Test

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Question 1 of 5.

A linear relationship between the quantities x and y is represented in the preceding table for certain values of x. Which of the following equations models the relationship between x and y?

A. y = 3/2x + 9

B. y = 2/3x + 9

C. y = -3/2x + 9

D. y = -2/3x + 9

Explanation: To determine the equation that models the linear relationship between 2 and y, we first calculate the slope ( m) using the formula m -Taking the points (0,9) and (3, 11) from the table, the slope is . Next, we identify the y-intercept (b), which is the value of y when x = 0. From the table, when y = 9, so b = 9. Substituting these values into the slope-intercept form y = mx + b, we get To verify, substitute another point: for (6, 13), y = 2/3 * (6) + 9 = 13 which matches. Similarly, for (9, 15), it gives 15. Thus, the correct equation is y = 2/3 * x + 9.

Question 2 of 5.

Which of the following is an equation?

A. x = 2

B. xÂ²+xy-y

C. 3x - 4 = 20y^2

D. 13y = y + 1

E. x/5 = 9

Explanation: An equation is a statement that two expressions are equal, containing an equals sign. x=2 is an equation. xÂ²+xy-y is an expression, not an equation. 3x-4=20y^2 is an equation. 13y=y+1 is an equation. x/5=9 is an equation. Therefore, the equations are A, C, D, and E.

Question 3 of 5.

Which of the following best describes the expression shown?

A. The expression has two terms, none of which are constants.

B. The expression has two terms, one of which is a constant.

C. The expression has three terms, one of which is a constant.

D. The expression has three terms, all of which are constants.

Explanation: The expression has three terms: 5xÂ², 2x, and -2. The term -2 is a constant. Option A is incorrect because there are three terms and one is a constant. Option B is wrong as there are three terms. Option D is incorrect because not all terms are constants; 5xÂ² and 2x are variable terms.

Question 4 of 5.

Which of the following lists contains all the coefficients of the expression 12x^3 + 7x^2 + 24x?

A. 2, 3

B. 7, 12

C. 7, 12, 24

D. 2, 3, 7, 12, 24

Explanation: Coefficients are the numerical factors of the terms. For 12xÂ³, the coefficient is 12; for 7xÂ², it is 7; for 24x, it is 24. So the coefficients are 12, 7, and 24. Option A lists digits from the exponents. Option B misses 24. Option D includes digits that are not coefficients.

Question 5 of 5.

In terms of x, what is the sum of the lengths of the sides of the preceding polygon?

A. 18x-22

B. 21x-5

C. 23x+32

D. 19x-2

Explanation: To find the sum of the lengths of the sides of the polygon, we first identify the given side lengths: AB = 10- 2x, BC = x+3, CD=4x-5, DE = 6x-7, EF = 62-5, and FA = 42 +2. Next, we add these expressions together: (10-2)+(x+3)+(4x-5)+(6x-7)+(6x-5)+(4x+2). Combining like terms, we group all coefficients of a and constant values: (-2x+x+4x+6x+6x+ 4x)+(10+3-5-7-5+2). Simplifying further, the coefficient of adds up to 192, while the constants simplify to -2. Therefore, the total sum of the lengths of all the sides of the polygon is 19 - 2. This expression represents the perimeter of the polygon in terms of 2.