Sonny has entered a reading contest at the local library. After reading two books, he has read 396000 words of text. After five books, he has read 990000 words of text. Write a linear function in slope-intercept form to model his progress where x is the number of books read and y is the total number of words read.

y=

How many books will he need to read to reach a total of 10,000,000 words?

Please check the expalantion.

Step-by-step explanation:

Let

Given that:

After reading two books, he has read 396000 words of text.

After five books, he has read 990000 words of text.

As the function is linear, so we take the points

Determining the slope between (2, 396000) and (5, 990000)

(x₁, y₁) = (2, 396000)

(x₂, y₂) = (5, 990000)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [990000 - 396000] / [5 - 2]

               = 594000 / 3  

               = 198000

Thus, the slope of the line = m = 198000

substituting the point (2, 396000) and m = 198000 in the slope-intercept form of the linear equation to determine the y-intercept

y = mx+b

396000 = 198000(2) + b

flipe the equation

198000(2) + b = 396000

396000 + b = 396000

subtracting 396000 from both sides

396000 + b - 396000 = 396000 - 396000

b = 0

now substituting b = 0 and m = 198000 in the slope-intercept form of the linear equation to determine the y-intercept

y = mx+b

y = 198000x + 0

y = 198000x

Therefore, a linear function in slope-intercept form to model his progress is:

y = 198000x

Part b)

How many books will he need to read to reach a total of 10,000,000 words?

As we have already determined a linear function in slope-intercept form to model his progress.

y = 198000x

substituting y = 10,000,000 in the equation

y = 198000x

10,000,000 =  198000x

flip the equation

198000x = 10,000,000

dividing the both equation by 198000

198000x/198000 = 10,000,000/198000

x = 50.5

Thus, Sonny will need to read 50.5 books to read to reach a total of 10,000,000 words.  

  n=   0.0000 - 0.3750 i  

  n=   0.0000 + 0.3750 i

step-by-step explanation:

one of these should be correct