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.

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facundo3141592 facundo3141592 · Answer 1 · 2022-02-07T11:10:07+01:00

The coefficients of the linear equation are:

This means that the correct options are B and E.

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:

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