Question

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: A graph titled Harry’s Book Reading shows Number of Weeks on the x-axis and Number of Pages Left on the y-axis. The scale on the x-axis shows numbers from 0 to 6 at increments of 1, and the scale on the y-axis shows numbers from 0 to 385 at increments of 55. A straight line joins the ordered pairs 0, 275 and 1, 220 and 2, 165 and 3, 110 and 4, 55 and 5, 0. Which equation best models the relationship between x and y? y = −5x + 55 y = −55x + 385 y = −5x + 275 y = −55x + 275

Answer 1

Answer:

• $y=-55x+275$

Explanation:

The given points are:

• (0, 275)
• (1, 220)
• (2, 165)
• (3, 110)
• (4,55)
• (5, 0)

Since a straight line joins all the points, the equation that models the relationship is linear and you can find the slope-intercept equation which has the general form:

             $y=mx+b$

Where:

             $m$  is the slope

             $b$  is the y-intercept

1. Find the slope

You can use any two ordered pairs.

• m = rise/run = Δy/Δx = [220 - 275] /[1 - 0] = - 55

2. Find the y-intercept

The y-intercept is the value of y when x = 0; thus it is 275.

• b = 275

3. Substitute in the slope-intercept equation

• $y=-55x+275$

That is the last option.