Question

Shyryia read a book cover to cover in a single session, at a constant rate. After reading for 1.5 hours, she had 402 out of the total 480 pages left to read. Let y represent the number of pages left to read after x hours.

Complete the equation for the relationship between the number of pages left and number of hours.

Answer 1

-52x+480.

Explanation:

I took the test, definitely correct

Answer 2

`y=-52x+480`

Explanation:

Linear Modeling

Some events can be modeled as linear functions. If there is a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The linear function can be expressed in the slope-intercept format:

`y=mx+b`

The event into consideration is the number of pages of a book left to read by Shyryia.

We know that for x=1.5 hours, she had y=402 out of the total 480 pages left to read. This is the point ( 1.5, 402 ). The other point is not obvious but can be inferred by context. If she hasn't used any time to read (x=0), then she would have y=480 pages left to read. This is the point (0,480).

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

`\displaystyle y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Substituting the given points:

`\displaystyle y-402=(402-480)/(1.5-0)(x-1.5)`

`\displaystyle y-402=(-78)/(1.5)(x-1.5)`

Operating:

`y-402=-52(x-1.5)`

`\mathbf{y=-52x+480}`