Algebra I Flashcards

Which of the following represents a linear function?

Answer: y = 2x + 3

A linear function has the form y = mx + b; y = 2x + 3 fits this form with m = 2 and b = 3.

What is the y-intercept of the equation y = 3x - 7?

Answer: -7

In slope-intercept form y = mx + b, the y-intercept is b, which equals -7.

Solve for x: 2(x - 3) = 10.

Answer: 8

Distributing gives 2x - 6 = 10; adding 6 gives 2x = 16; dividing by 2 gives x = 8.

Which ordered pair is a solution to the system: y = x + 2 and y = -x + 6?

Answer: (2, 4)

For (2, 4): y = 2 + 2 = 4 and y = -2 + 6 = 4, so (2, 4) satisfies both equations.

Factor the expression x² - 9.

Answer: (x + 3)(x - 3)

x² - 9 is a difference of squares: a² - b² = (a + b)(a - b), so x² - 9 = (x + 3)(x - 3).

What does the slope of a linear equation represent on a graph?

Answer: The rate of change of y with respect to x

Slope measures the rate of change, showing how much y changes for each unit increase in x.