Question

A. Determine and then compare the rate of change (slope) for each function in terms of the quantities compared.b. Determine and the compare the y-intercept of each function in terms of the quantities.

Answer 1

A.

Pavilion's line:

`y=10x+50`

The slope of the line is the coefficient multiplying x, so it is m=10

Heliophobia's line:

To determine the slope of this line you have to use the following formula:

`m_p=(y_1-y_2)/(x_1-x_2)`

Where

(x₁,y₁) are the coordinates of one point on the line

(x₂,y₂) are the coordinates of a second point on the line

I'll choose to use points (1,85) and (0,70) but you can use any pair of points on the given line:

`m_h=(85-70)/(1-0)=(15)/(1)=15`

The slope of the Pavillion's line is m=10 → it indicates that y increases 10 units for every unit increase of x.

The slope of the Heliophobia's line is m=15 → it indicates that y increases 15 units for every unit increase of x.

The increase of Heliophobia's line is greater than the increase of Pavillion's line.

B.

The y-intercept is the value of y when x=0

For Pavillion's line the y-intercept is

`\begin{gathered} y=10\cdot0+50 \\ y=50 \end{gathered}`

The coordinates are (0, 50)

For the Heliophobia's line the y-intercept is given in the table (0,70)