Question

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.

Answer 1

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:

$a = \frac{y_2 - y_1}{x_2 - x_1}$

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

(1, 8) and (1.5 , 10.1)

Then the rate of change is:

$a = \frac{10.1 - 8}{1.5 - 1} = 4.2$

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:

brainly.com/question/4025726