Answered

From personal advice to professional guidance, IDNLearn.com has the answers you seek. Join our community to receive prompt, thorough responses from knowledgeable experts.

Myra has a remote-controlled toy boat. She runs the toy boat on a lake at a constant speed. The graph of a function representing the toy boat’s distance, y, in feet, from the shore of the lake after x seconds includes the points (1, 8) and (1.5, 10.1).
Which statements are TRUE? Select all that apply.
A
The initial value of the function is 8.
B
The rate of change of the function is 4.2.
C
The equation for the function is y=3.8x+4.2 .
D
The toy boat’s speed on the lake is 4.2 feet per second.
E
The toy boat is originally 3.8 feet from the shore of the lake.

Sagot :

Facundo3141592idn

The coefficients of the linear equation are:

  • Rate of change = 4.2
  • Initial value = 3.8

This means that the correct options are B and E.

How we can find the linear equation?

First, a general linear equation is written as:

y = a*x + b

Where a is the rate of change (also called slope) and b is the y-intercept (also called initial value).

If we know that the line passes through two points (x₁, y₁) and (x₂, y₂), then the rate of change is given by:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

In this case, we know that the line passes through:

(1, 8) and (1.5 , 10.1)

Then the rate of change is:

[tex]a = \frac{10.1 - 8}{1.5 - 1} = 4.2[/tex]

So the line is something of the form:

y = 4.2*x + b

To find the value of b we can use one of the given points, I will use (1, 8).

This means that when x =1, we have y = 8, replacing that we get:

8 = 4.2*1 + b

8 - 4.2 = b

3.8 = b

So we have:

  • Rate of change = 4.2
  • Initial value = 3.8

Then the correct options are:

B and E.

If you want to learn more about linear equations, you can read:

https://brainly.com/question/4025726

Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! IDNLearn.com has the solutions you’re looking for. Thanks for visiting, and see you next time for more reliable information.