We have been given that between 1985 and 1992, 15 stamps were added to your stamp collection. In 1990, you had 130 stamps.
Also, we are given that x=0 corresponds to year 1985.
Since we are given that 15 stamps were added between the years 1985 to 1992. Therefore, we can find the number of stamps added per year (slope) as:
[tex]Slope(m)=\frac{15}{1992-1985}=\frac{15}{7}[/tex]
Therefore, we can express the equation of our linear model as"
[tex]y=mx+b\\
y=\frac{15}{7}x+b[/tex]
Now we can use the fact that total number of stamps in year 1990 were 130 to find the value of b.
x = 5 corresponds to year 1990.
Thus, we get:
[tex]130=\frac{15}{7}(5)+b\\
130=\frac{75}{7}+b\\
b=130-\frac{75}{7}\\
b=\frac{835}{7}[/tex]
Therefore, the required equation of our linear model is:
[tex]y=\frac{15}{7}x+\frac{835}{7}\\[/tex]
