Question

I'll send the pic in the session

Answer 1

The Slope-Intercept form of the equation of a line is:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

In this case you know that "y" represents the number of books in Himanshu's home library and "x" represents the number of weeks.

In the graph you can identify that:

`b=6`

And you can also identify this point on the line:

`\mleft(2,8\mright)`

Where:

`\begin{gathered} x=2 \\ y=8 \end{gathered}`

Substitute these values into the equation

`y=mx+b`

and solve for "m" in order to find the slope:

`\begin{gathered} 8=(m)(2)+6 \\ 8-6=2m \\ \\ (2)/(2)=m \\ \\ m=1 \end{gathered}`

Then, the equation of this line is:

`y=x+6`

Based on the explained above, you can conclude that he had 6 books in his library and then he started adding 1 book each week.

To find the number of books he has after 4 weeks, you can make:

`x=4`

Substitute this value into the equation and evaluate. Then:

`y=(4)+6=10`

The answer is: Option A and Option F.