Mark reads 42 pages of a book every 3/4 hour. Write an equation that models the relationships between x, the number of hours Mark reads, and , y the number of pages of the book he reads.

Answer:The equation that models the relationships between [tex]x[/tex], the number of hours Mark reads, and , [tex]y[/tex] the number of pages of the book he reads is:[tex]y=56x[/tex]Step-by-step explanation:Given:Mark reads 42 pages every [tex]\frac{3}{4}[/tex] hour.The number of hours is given by = [tex]x[/tex]The number of pages is given by =[tex]y[/tex]The equation can be modeled as:[tex]y=mx+b[/tex]where [tex]m[/tex] represents rate of change and [tex]b[/tex] represents the y-intercept or the initial value.Rate of change =[tex]=\frac{Change\ in\ y}{Change\ in\ x}=\frac{42}{\frac{3}{4}}=42\times \frac{4}{3}=56[/tex]The initial value [tex]b=0[/tex] as Mark starts reading from 0.So, the equation is:[tex]y=56x[/tex]