Question

(50 points to answer 3 questions)

Harry reads equal numbers of pages of a book every week. The graph shows the number of pages of the book left to read, y, after x weeks: (graph at the bottom)

Which equation best models the relationship between x and y?

y = −5x + 55
y = −55x + 385
y = −5x + 275
y = −55x + 275

What is the initial value of the function represented by this graph?

A coordinate grid is shown with x- and y-axes labeled from 0 to 7 at increments of 1. A straight line joins the ordered pair 0, 5 with the ordered pair 7, 7. (graph at the bottom)

0
4
5
7

Mike is cycling from the library to his home. The equation shows Mike's distance (y), in miles, from his home after x minutes:

y = 12 − 2x

What does the number 12 in the equation represent?

The speed at which Mike is cycling
The rate of change of Mike's speed
Mike's distance from home when he begins cycling
Mike's distance from the library when he begins cycling

Answer 1

Answer:y = −55x + 275

Explanation:

Answer 2

y = −55x + 275

The initial value is 5

Mike's distance from home when he begins cycling

Explanation:

The equation of a line is

y= mx+b where m is the slope and b is the y intercept

The y intercept is 275

Two points are (0,275) and (5,0)

The slope is (y2-y1)/(x2-x1) = (0-275)/(5-0) = -275/5 =-55

y = -55x+275

The initial value is when x = 0

When x = 0 , y = 5

y = 12-2x

Rewriting

y = -2x+12

This is in the form y = mx +b where the slope is -2 and the y intercept is 12

12 is the initial value or when x = 0. It would be the distance that he needs to cover. He needs to go from the library to his house.