In a linear function that describes a real - world situation, what part of the function corresponds to the initial value?

Question

a. the x - value when y = 1
b. the y - intercept
c. the y - value when x = 1
d. the x - intercept

Answer 1

In a linear function, the part of the function that corresponds to the initial value is:

b. the y - intercept

The y-intercept represents the value of the function when the independent variable (x) is equal to zero, which is typically interpreted as the initial value in real-world situations.

Answer 2

You are taking a road trip across several states. Your distance from your final destination is modeled with the equation
f (x) = -350x + 1,400, where x represents the number of days you have been traveling. Identify and interpret the initial value.

a. the initial value of 1,400 represents the distance from your starting point to your final destination.
b. the initial value of 350 represents the distance from your starting point to your final destination.
c. the initial value of 1,400 represents the distance you travel each day.
d. The initial value of 350 represents the distance you travel each day.

Answer 3

In the given function $f(x)=-350x+1,400$, the initial value is represented by the constant term when $x=0$.

When $x=0$:

$$f(0)=-350(0)+1,400=1,400$$

This initial value of 1,400 represents the distance from your starting point to your final destination at the beginning of your trip (when no days have passed).

Therefore, the correct interpretation is:

a. the initial value of 1,400 represents the distance from your starting point to your final destination.

Answer 4

Marie orders a shuttle to the airport and learns that it will cost $15 plus $0. 50 per mile. Write the equation of a linear function that models the relationship between number of miles and total cost of the shuttle.

a. y = x + 7.5, where x is the number of miles and y is the total cost of the shuttle.
b. y = 15x + 0.5, where x is the number of miles and y is the total cost of the shuttle.
c. y = 0.5x + 15, where x is the number of miles and y is the total cost of the shuttle.
d. y = 7.5x, where x is the number if miles and y is the total cost of the shuttle.

Answer 5

To model the relationship between the number of miles and the total cost of the shuttle, we can represent the total cost as a linear function. The cost consists of a fixed fee of $15 plus an additional charge of $0.50 per mile.

Let $x$ be the number of miles and $y$ be the total cost of the shuttle. The equation can be written as:

$$y=0.50x+15$$

This means for every mile traveled (represented by $x$), you add $0.50 to the fixed cost of $15.

Thus, the correct option is:

c. $y=0.5x+15$, where $x$ is the number of miles and $y$ is the total cost of the shuttle.

Answer 6

Use the image to answer the question.
Linear Function 1: (2,12) (1, 9)

Linear Function 2: x y
0 2
5 42

Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change?

a. Linear Function 1 has the greater rate of change, with a rate of changel equal to 6 while Linear Function 2 has a rate of change equal to 2.
b. Linear Function 1 has the greater rate of change, with a rate of change equal to 3 while Linear Function 2 has a rate of change equal to 2.
c. Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear function 1 has a rate of change equal to 6.
d.Linear Function 2 has the greater rate of change, with a rate change equal to 8 while Linear Function 1 has a rate of change equal to 3.

Answer 7

To find the rate of change for each linear function, we'll calculate the slope (rate of change) using the slope formula:

$$\text{slope}=\frac{y_2-y_1}{x_2-x_1}$$

For Linear Function 1:

The points are $(2,12)$ and $(1,9)$.

Using the slope formula: $$\text{slope}=\frac{12-9}{2-1}=\frac{3}{1}=3$$

For Linear Function 2:

The points are $(0,2)$ and $(5,42)$.

Using the slope formula: $$\text{slope}=\frac{42-2}{5-0}=\frac{40}{5}=8$$

Comparison of Rates of Change:

• Linear Function 1 has a rate of change of 3.
• Linear Function 2 has a rate of change of 8.

Therefore, the statement that is correct is:

c. Linear Function 2 has the greater rate of change, with a rate of change equal to 8 while Linear Function 1 has a rate of change equal to 3.

Answer 8

Identify the slope and y-intercept of the equation: y= -1/2x + 2.
*
1 point
Slope: 1/2 Y-Intercept: 2
Slope: -1/2 Y-Intercept: 2
Slope: 2 Y-Intercept: 1/2
Slope: 2 Y-Intercept: -1/2

Answer 9

The given equation is in the slope-intercept form, which is typically expressed as:

$$y=mx+b$$

where:

• $m$ is the slope,
• $b$ is the y-intercept.

For the equation $y=-\frac{1}{2}x+2$:

• The slope $m$ is $-\frac{1}{2}$.
• The y-intercept $b$ is $2$.

Thus, the correct identification is:

Slope: -1/2 Y-Intercept: 2