Diagnostic Algebra and Algebraic Thinking Flashcards

Which table of values represents the linear equation y = 2x − 1?

Answer: x=1→1, x=2→3, x=3→5

Using y = 2x − 1: when x=1, y=1; x=2, y=3; x=3, y=5.

Solve for y: 3y + 5 = 2y + 13

Answer: y = 8

Subtracting 2y and 5 from both sides: y = 8.

A car travels at a constant speed of 60 mph. Which expression gives the distance (d) traveled in t hours?

Answer: d = 60t

Distance equals rate times time, so d = 60t.

What is the slope of a line that passes through (2, 3) and (6, 11)?

Answer: 2

Slope = (11 − 3) ÷ (6 − 2) = 8 ÷ 4 = 2.

Which of the following is NOT a function?

Answer: {(1,2),(1,4),(2,6)}

A relation is not a function when one x-value maps to more than one y-value; x=1 maps to both 2 and 4.

Simplify: 3x + 2y − x + 5y

Answer: 2x + 7y

Combining like terms: (3x − x) + (2y + 5y) = 2x + 7y.

The sum of two consecutive integers is 47. What are the integers?

Answer: 23 and 24

If the integers are n and n+1, then 2n+1=47, so n=23 and n+1=24.