Question

Use the ordered pairs to write a function rule. Give the rule in the slope-intercept form.

Answer 1

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.

Answer 2

$y=\frac{-1}{4}x-\frac{3}{2}$