Answer:
Please check the expalantion.
Step-by-step explanation:
Let
- x is the number of books read
- y is the total number of words read
Given that:
After reading two books, he has read 396000 words of text.
- Thus, we get the point (2, 396000).
After five books, he has read 990000 words of text.
- Thus, we get the point (5, 990000).
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.
