Question

Angelica reads 15 pages of a book each day. In 10 days, she reads 200 pages. Assume the relationship is linear. Find and interpret the rate of change and initial value.
help me please

Answer 1

Given:

Angelica reads 15 pages of a book each day.

In 10 days, she reads 200 pages.

Assume the relationship is linear.

To find:

The rate of change and initial value.

Solution:

The slope intercept form of a linear function is:

$y=mx+b$            ...(i)

Where m is the slope and b is the y-intercept.

Angelica reads 15 pages of a book each day. So, the rate of change is 15 pages per day and $m=15$.

In 10 days, she reads 200 pages. It means the linear relation passes through the point (10,200).

Putting $x=10,y=200,m=15$ in (i), we get

$200=15(10)+b$

$200=150+b$

$200-150=b$

$50=b$

So, the y-intercept is 50. It means the initial number of pages angelica already read is 50.

Therefore, the rate of change is 15, it means Angelica reads 15 pages per day. The y-intercept is 50, it means the initial number of pages angelica already read is 50.