To get the y-intercept of the function, let us attempt to write out the function in the slope-intercept form.
The slope-intercept form of a linear equation is given to be:
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
To calculate the slope, let us make use of the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We can pick any 2 ordered points from the table, such that:
[tex]\begin{gathered} (x_1,y_1)=(1,6) \\ (x_2,y_2)=(2,3) \end{gathered}[/tex]
Therefore, we can calculate the slope to be:
[tex]m=\frac{3-6}{2-1}=\frac{-3}{1}=-3[/tex]
Hence, the equation of the line will look like this:
[tex]y=-3x+b[/tex]
We can get the value of b by substituting the ordered pair (1, 6) into the equation:
[tex]\begin{gathered} 6=-3(1)+b \\ b=6+3 \\ b=9 \end{gathered}[/tex]
ANSWER
The equation of the line is gotten to be:
[tex]y=-3x+9[/tex]
Hence, the y-intercept is 9.
The correct option is OPTION B.
