Respuesta :
Given:
f(1) = 1 and f(-3) = 17
To find:
The lines function f.
Solution:
If f(a) = b, it means the function f passes through (a,b).
Here, f(1) = 1, it means the function f passes through (1,1).
f(-3) = 17, it means the function f passes through (-3,17).
If a linear function passes through two point [tex](x_1,y_1)\text{ and }(x_2,y_2)[/tex], then the equation of line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The linear function f passes through (1,1) amd (-3,17). So, the equation of linear function is
[tex]y-1=\dfrac{17-1}{-3-1}(x-1)[/tex]
[tex]y-1=\dfrac{16}{-4}(x-1)[/tex]
[tex]y-1=-4(x-1)[/tex]
[tex]y-1=-4x+4[/tex]
Add 1 on both sides.
[tex]y-1+1=-4x+4+1[/tex]
[tex]y=-4x+5[/tex]
Put y=f(x), to write in function notation.
[tex]f(x)=-4x+5[/tex]
Therefore, required lines function is [tex]f(x)=-4x+5[/tex].
