Respuesta :
The Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
Knowing that:
[tex]\begin{gathered} f\mleft(-2\mright)=0 \\ f(6)=-4 \end{gathered}[/tex]You can identify that the line passes through these points:
[tex]\begin{gathered} (-2,0) \\ (6,-4) \end{gathered}[/tex]By definition, the value of "x" is zero when the line intersects the y-axis and the value of "y" is zero when the line intersects the x-axis.
To find the slope of a line you can use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, you can set up that:
[tex]\begin{gathered} y_2=-4 \\ y_1=0 \\ x_2=6 \\ x_1=-2 \end{gathered}[/tex]Then substituting values into the formula and evaluating, you get that the slope of the line is:
[tex]m=\frac{-4-0}{6-(-2)}=\frac{-4}{6+2}=\frac{-4}{8}=-\frac{1}{2}[/tex]You can substitute the slope and the coordinates of the second point into the equation
[tex]y=mx+b[/tex]and then solve for "b":
[tex]\begin{gathered} -4=-\frac{1}{2}(6)+b \\ \\ -4=-3+b \\ -4+3=b \\ b=-1 \end{gathered}[/tex]Knowing "m" and "b", you can write the following equation of this line in Slope-Intercept form:
[tex]y=-\frac{1}{2}x-1[/tex]Rewriting it with:
[tex]f(x)=y[/tex]You get that the answer is:
[tex]f(x)=-\frac{1}{2}x-1[/tex]