Algebra: Linear Equations/Inequalities Flashcards

What is the slope of the line passing through (2, 5) and (6, 13)?

Answer: 2

Slope = (13 − 5) / (6 − 2) = 8 / 4 = 2.

If −3x + 2 ≤ 14, which describes the solution?

Answer: x ≥ −4

Subtract 2: −3x ≤ 12; divide by −3 and flip the inequality: x ≥ −4.

A store sells notebooks for $2.50 each. Sarah has $20 to spend. Which inequality models the number of notebooks n she can buy?

Answer: 2.50n ≤ 20

Sarah can spend at most $20, so the total cost 2.50n must be less than or equal to 20.

Solve for x: 7x − 4 = 3x + 16

Answer: x = 5

Subtract 3x from both sides: 4x − 4 = 16; add 4: 4x = 20; divide: x = 5.

Which point lies on the line y = −2x + 8?

Answer: (4, 0)

Substituting x = 4: y = −2(4) + 8 = −8 + 8 = 0, so (4, 0) is on the line.

A temperature in Celsius C is related to Fahrenheit F by F = (9/5)C + 32. What is F when C = 20?

Answer: 68°F

F = (9/5)(20) + 32 = 36 + 32 = 68°F.

Which pair of equations represents the same line?

Answer: y = x + 4 and 2y = 2x + 8

Dividing 2y = 2x + 8 by 2 gives y = x + 4, which is identical to the first equation.