You are given four ordered pairs (–12, 1.5), (−1, –1.25), (5, –2.75), (8, −3.5). You can rewrite them as a function in following way:
f(-12)=1.5,
f(-1)=-1.25,
f(5)=-2.75,
f(8)=-3.5.
The slope-intercept rule has aform f(x)=mx+b, where m and b are constants. Find them:
1. f(-12)=m·(-12)+b=1.5,
2. f(-1)=m·(-1)+b=-1.25.
You get the system of two linear equations:
\(\left\{\begin{array}{l}-12m+b=1.5\\ \\-m+b=-1.25.\end{array}\right.\)
Subtract from the second equation the first one:
\(-m+b-(-12m+b)=-1.25-1.5,\\ \\-m+b+12m-b=-2.75,\\ \\11m=-2.75,\\ \\m=-0.25.\)
Then
-(-0.25)+b=-1.25,
b=-1.25-0.25,
b=-1.5
The slope-intercept rule for the function is f(x)=-0.25x-1.5.
