Given: A line passing through points (1,-13) and (-10,31).
Required: To determine the y-intercept of the line.
Explanation: The slope of the line is given by the formula-
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the values and further solving as follows-
[tex]\begin{gathered} m=\frac{31-(-13)}{-10-1} \\ =\frac{44}{-11} \\ =-4 \end{gathered}[/tex]
Thus the equation of the line is-
[tex]y+13=-4(x-1)[/tex]
To get the y-intercept, substitute x=0 as follows-
[tex]\begin{gathered} y+13=4 \\ y=-9 \end{gathered}[/tex]
Final Answer: Option F is correct.
