Question

A balloon artist creates balloon hats for children at a store’s grand opening. The graph shows the number of balloons the artist has remaining, y, after creating x hats.
What phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created? Check all that apply.

positive slope
negative slope
zero slope
constant slope
increasing function
decreasing function

Answer 1

Answer:

The phrase that best describes the the line representing the relationship between the number of balloons remaining and the number of hats created is:

• Negative slope.
• Constant slope.

• Decreasing function.

Step-by-step explanation:

We are given a graph that represents the relationship between the Number of Balloons Hats and the number of balloons remaining.

Clearly from the graph we could that it is  a linear function.

Also, the function is a decreasing function since with the increase of one variable that is the number of Balloon hats produced the other variable i.e. Balloons remaining is decreasing.

Also, we can calculate the slope of the line.

as the line is passing through (0,500) and (100,0)

Hence, the slope of line is:

$Slope=\dfrac{0-500}{100-0}\\\\Slope=\dfrac{-500}{100}\\\\Slope=-5$

Hence, the graph has a negative slope.

Also, we know that a slope of a line is always constant.

So, the correct statements are:

Negative slope.

Constant slope.

Decreasing function.

Answer 2

Answer:

The line has a negative slope

The line has a constant slope

The function is decreasing function.

Step-by-step explanation:

Given is a graph showing the number of balloons the artist has remaining, y and x is the no of hats created.

The graph shown is a straight line passing through (0,500) amd (100,0)

Hence in intercept form we can write the equation as

$\frac{x}{100} +\frac{y}{500} =1$

Slope of this line = $\frac{-1/100}{1/500} =-5$

Since slope is negative, we find that when x increases y decreases and vice versa

Hence answers would be

The line has a negative slope

The line has a constant slope

The function is decreasing function.