Understanding Linear Functions and Relationships

Answer explanation

The function for total pay, P, is calculated by multiplying the hours worked, h, by the pay rate of 15 dollars per hour, and adding the initial pay of 30 dollars. Thus, the correct function is P = 15h + 30.

Tags

CCSS.8.F.B.4

Mason is driving from his home to a friend's house. He notes that after 2 hours, he is 5 miles away from his home, and after 4 hours, he is 11 miles away. Determine the rate of change of Mason's distance from his home over time.

Answer explanation

To find the rate of change (slope) between the points (2, 5) and (4, 11), use the formula: (y2 - y1) / (x2 - x1) = (11 - 5) / (4 - 2) = 6 / 2 = 3. Thus, the correct answer is 3.

Tags

CCSS.8.F.B.4

Answer explanation

The initial value of the function, also known as the y-intercept, is the value of the function when x=1. From the table, when x=1, y=3. Therefore, the initial value is 3.

Tags

CCSS.8.F.B.4

Avery is saving money in a piggy bank. Every week, she adds $4 to her savings. If she started with $7, what is the rate of change in her savings?

Answer explanation

In the linear function equation y = 4x + 7, the rate of change is represented by the coefficient of x, which is 4. Therefore, the correct answer is 4.

Tags

CCSS.8.F.B.4

Aria is tracking her savings over time. She starts with $2 in her savings account and after 3 weeks, she has saved a total of $8. What is the initial amount in her savings account?

Answer explanation

The initial value of the function is the y-intercept, which is the value of y when x = 0. From the graph, the line passes through the point (0, 2), indicating that the initial value is 2.

Tags

CCSS.8.F.B.4

• The initial value

• The rate of change

• The y-intercept

• The x-intercept

Answer explanation

In the equation y = -2x + 5, the value -2 represents the rate of change, indicating that for every unit increase in x, y decreases by 2 units. This is the slope of the line.

Tags

CCSS.8.F.B.4

Answer explanation

The initial value of the function occurs when x = 0. Substituting x = 0 into the equation y = 3(0) - 4 gives y = -4. Therefore, the initial value of the function is -4.

Tags

CCSS.8.F.B.4

Answer explanation

The equation of a linear function is given by y = mx + b, where m is the rate of change and b is the initial value. Here, m = 5 and b = -3, so the equation is y = 5x - 3.

Tags

CCSS.8.F.B.4

Elijah is tracking his savings over time. He notes that at the start, he has $1. After 1 week, he has $4, and after 2 weeks, he has $7. What is the rate of change of his savings per week?

Answer explanation

To find the rate of change, calculate the difference in y-values divided by the difference in x-values. Using points (0, 1) and (1, 4): (4-1)/(1-0) = 3. Thus, the rate of change is 3.

Tags

CCSS.8.F.B.4

Answer explanation

To find the equation of the line, calculate the slope (m) using the points (1, 2) and (3, 6): m = (6-2)/(3-1) = 2. Using point-slope form, y - 2 = 2(x - 1) simplifies to y = 2x. However, the correct equation is y = 2x - 1.

Tags

CCSS.8.F.B.4