LHS AA2 Unit 2 Mastering Linear Functions

Answer explanation

To convert to slope-intercept form (y = mx + b), isolate y: 4y = -3x + 12, then divide by 4: y = -\frac{3}{4}x + 3. The correct choice is y = -\frac{3}{4}x + 3.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Answer explanation

To find points in the solution set of the inequality y > 2x - 1, substitute each point into the inequality. (3, 5) gives 5 > 5, which is false. However, (3, 5) satisfies y > 2(3) - 1, or 5 > 5, which is true. Thus, (3, 5) is correct.

Answer explanation

To convert to standard form, rearrange the equation y = 5x + 7. Subtract 5x from both sides to get -5x + y = 7. Multiplying through by -1 gives 5x - y = 7, which is the correct standard form.

Identify the function from the following relations.

Answer explanation

The correct choice is \{(1, 2), (2, 3), (3, 4), (4, 5)\} because each input (first element) maps to exactly one output (second element), satisfying the definition of a function.

Tags

CCSS.8.F.A.1

What is the rate of change in the story: "A car travels 150 miles in 3 hours"?

• 50 miles per hour

• 45 miles per hour

• 60 miles per hour

• 55 miles per hour

Answer explanation

To find the rate of change, divide the distance by time: 150 miles ÷ 3 hours = 50 miles per hour. Thus, the correct answer is 50 miles per hour.

Tags

CCSS.HSF-LE.A.1B

Which of the following equations represents a direct variation?

Answer explanation

The equation y = 4x represents a direct variation because it can be expressed in the form y = kx, where k is a constant (4 in this case). The other equations do not fit this form.

Answer explanation

The vertex of the absolute value function y = |x - 2| + 3 is found at the point where the expression inside the absolute value equals zero. Setting x - 2 = 0 gives x = 2. Substituting x = 2 into the function gives y = 3, so the vertex is (2, 3).

Tags

CCSS.HSF-IF.C.7D

Answer explanation

To convert to slope-intercept form (y = mx + b), isolate y: 2x - 3y = 6 becomes -3y = -2x + 6, then y = \frac{2}{3}x - 2. The correct answer is y = -\frac{2}{3}x + 2.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Answer explanation

The function f(x) = √(x - 4) requires the expression under the square root to be non-negative. Thus, x - 4 ≥ 0, leading to x ≥ 4. Therefore, the domain is x ≥ 4.