Ultimate Regents Algebra Flashcards

The graph of a line passes through (0, -4) and (3, 2). What is the equation of the line?

Answer: y = 2x - 4

Slope = (2 - (-4))/(3 - 0) = 6/3 = 2; y-intercept is -4, so y = 2x - 4.

What is the solution set of |2x - 3| = 7?

Answer: x = 5 or x = -2

2x - 3 = 7 gives x = 5, and 2x - 3 = -7 gives x = -2.

A rectangle has length (x + 5) and width (x - 2). Which expression represents its area?

Answer: x² + 3x - 10

Using FOIL: (x+5)(x-2) = x² - 2x + 5x - 10 = x² + 3x - 10.

What is the value of x in the system: 3x + y = 11 and x - y = 1?

Answer: 3

Adding the equations: 4x = 12, so x = 3.

Which describes an exponential decay function?

Answer: f(x) = 500(0.85)ˣ

A base between 0 and 1 (0.85) produces exponential decay.

Factor completely: x² - 49

Answer: (x + 7)(x - 7)

This is a difference of two perfect squares: x² - 49 = (x + 7)(x - 7).

The table shows a relation. Which ordered pair would make this relation NOT a function? {(1,3), (2,5), (3,7), (?,9)}

Answer: (2, 9)

If x = 2 is repeated with a different y-value, the relation fails the vertical line test and is not a function.