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

Let's see what to do buddy....

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1) Go...

We have the following equation for finding the slope of the line by using two points :

`slope = m = (y(b) - y(a))/(x(b) - x(a)) \\`

Where a and b are the points which the line through them.

We have points C and D here ,

So :

`slope = m = (y(d) - y(c))/(x(d) - x(c)) \\`

D = ( 7 , 12 ) and C = ( 0 , 0 )

Now just need to put the coordinates in the above equation :

`slope = m = (12 - 0)/(7 - 0) = (12)/(7) \\`

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2) Go...

We have the following equation to find the point-slope form of the linear functions :

`y - y(o) =(slope) * ( \: x - x(o) \: ) \\`

Where o is one of the given points.

So we must choose one of the points ,

I choose : D = ( 7 , 12 )

Then we have :

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

It's point-slope form, so we need to simplifies it to find slope-intercept form.

Look:

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

Both sides plus 12

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

Now we have the slope-intercept form of the CD line.

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3) Go...

Domain = [ 0 , 7 ]

Range = [ 0 , 12 ]

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And we're done.

Thanks for watching buddy good luck.

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