Question

#1.) What is the slope between point C and Point D? *Please Show All Work*

#2.) What is the equation of the line (Slope-Intercept Form: y = mx + b) that represents the climb from Point C to Point D? *Please Show All Work*

#3.) What is the domain and range the C to D part of the roller coaster?

Answer 1

1.
`m = slope = (12)/(7)`

2.
`y = (12)/(7)x`

3. Domain: 0≤x≤7

Range: 0≤y≤12

Explanation:

1. Assuming 1 unit = 1 box on the grid, therefore, coordinates of C and D would be:

C(0, 0),

D(7, 12)

`Slope = m = (y_2 - y_1)/(x_2 - x_1) = (12 - 0)/(7 - 0) = (12)/(7)`

2. Equation of the using the slope-intercept formula,
`y = mx + b`, where,

`m = slope = (12)/(7)`

b = y-intercept, which is where the line CD cuts the y-axis = 0

Plug in the values for m and b into the formula to get the equation of the line:

`y = (12)/(7)x + 0`

`y = (12)/(7)x`

3. The domain for C to D part = all x-values = 0≤x≤7

The range = all y-values = 0≤y≤12