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Find the linear function with the following properties.f( -4)= 7f( -8)= - 2answer : f (x) = ?

Sagot :

First, we find the slope

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where,

[tex]\begin{gathered} x_1=-4 \\ x_2=-8 \\ y_1=7 \\ y_2=-2 \end{gathered}[/tex][tex]m=\frac{-2-7}{-8-(-4)}=\frac{-9}{-8+4}=-\frac{9}{-4}=\frac{9}{4}[/tex]

Then, we use the point-slope formula to find the equation

[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-7=\frac{9}{4}(x-(-4)) \\ y-7=\frac{9}{4}x+9 \\ y=\frac{9}{4}x+9+7 \\ y=\frac{9}{4}x+16 \end{gathered}[/tex]

Hence, the function is

[tex]f(x)=\frac{9}{4}x+16[/tex]

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