Answer:
[tex]f(x)=-\frac{5}{2}x+5[/tex]
Step-by-step explanation:
The given points are (-4, 15), (0,5), (4,
-5), (8, -15)}
Let the linear function be [tex]f(x)=mx+b[/tex]
Using (0,5), we substitute have the y-intercept to be [tex]b=5[/tex]
The function now becomes: [tex]f(x)=mx+5[/tex]
Using (-4,15), we substitute x=-4, f(x)=15 to find m.
[tex]15=m*-4+5[/tex]
[tex]-4m=15-5[/tex]
[tex]-4m=10[/tex]
[tex]m=-\frac{10}{4}=-\frac{5}{2}[/tex]
The required linear function is [tex]f(x)=-\frac{5}{2}x+5[/tex]
