Question

A length of ribbon is cut into two pieces to use in a craft project. The graph shows the length of the second piece, x, for each length for the first piece, y.
A. How long is the ribbon? Explain how you know.

B. What is the slope of the line?

C. Explain what the slope of the line represents and why it fits the story.

Answer 1

Answer:

Part A) The length of the ribbon is 15 feet

Part B) $m=-1$

Part C) see the explanation

Step-by-step explanation:

Part A)

Let

x -----> the length of the second piece of ribbon in feet

y -----> the length of the first piece of ribbon in feet

we know that

The length of the ribbon is equal to the sum of the first piece and the second piece of ribbon

so

y+x

take any point from the graph

Example

(13,2)

That means

Second piece ----> x=13 ft

First piece ---->  y=2 ft

The length is (y+x)=2+13=15 ft

Part B) What is the slope of the line?

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

take the intercepts from the graph to calculate the slope

we have

(0,15) and (15,0)

substitute

$m=\frac{0-15}{15-0}$

$m=-1$

Part C) Explain what the slope of the line represents

we know that

The slope is equal to -1

That means, that we have a decreasing function, as the value of x (length of second piece) increases by one, the value of y (length of the first piece) decreases by one

The slope fits in the story because the linear equation in slope intercept form between the variable x and the variable y is equal to

$y=-x+15$