Question

Benji has read 5 books so far this year. Benji would like to graph the line that represents the total number of books he will have read, B, after m months, given that he reads 2.5 books each month. He would like the graph to show the number of books read for the next 10 months.

Answer 1

the 5 books would be the y intercept (b)

and 2.5 would be the slope (m)

y = mx +b

y = 2.5x + 5

B = 2.5 m + 5

Answer 2

Explanation:

The dependent variable in this situation is the total number of books read, B.  The number of books depends on the number of months, m; this means that months is the independent variable.

The independent variable goes along the x-axis and the dependent variable goes along the y-axis.

The y-intercept, the point where the data crosses the y-axis, is where x=0.  Since the independent variable is x, this means it is the number of books read at month 0 (before he starts keeping track).  This is 5.

The slope of the line, or rate of change, tells us how many books he plans to read each month.  This is 2.5.

Slope-intercept form of a line is y=mx+b, where m is the slope and b is the y-intercept.  Using the information in our problem, we have the equation

y = 2.5x + 5.

This line will go through the y-intercept at (0, 5).  The next point, at month 1, will be at the point (1, 7.5).  The line will increase by 2.5 books for every month it goes over; this means it will also go through the points (2, 10), (3, 12.5), and (4, 15).