Given:
The objective is to find f(-4).
Explanation:
The general equation of a straight line is,
[tex]y=mx+b\text{ . . . . .(1)}[/tex]
Here, m represents the slope of the straight line, b represents the y-intercept.
To find m:
The value of slope can be calculated by considering two coordinates from the graph,
[tex]\begin{gathered} (x_1,y_1)=(4,0) \\ (x_2,y_2)=(0,2) \end{gathered}[/tex]
On plugging the values in the formula of the slope,
[tex]\begin{gathered} m=\frac{2-0}{0-4} \\ =\frac{2}{-4} \\ =-\frac{1}{2} \end{gathered}[/tex]
Thus, the slope of the graph is -1/2.
From the graph, the y-intercept of the graph is 2.
On plugging the obtained values in equation (1),
[tex]y=-\frac{1}{2}x+2\text{ . . . . (2)}[/tex]
At x = -4 in equation (2),
[tex]\begin{gathered} f(-2)=-\frac{1}{2}(-2)+2 \\ =1+2 \\ =3 \end{gathered}[/tex]
Hence, the value of f(-4) is 3.
