SOLUTION: Suppose g is a linear function such that g(1.1)=3.3 and g(−2)=7.2. Find the equation for g.

Algebra ->  Linear-equations -> SOLUTION: Suppose g is a linear function such that g(1.1)=3.3 and g(−2)=7.2. Find the equation for g.      Log On


   

Question 1168508: Suppose g is a linear function such that g(1.1)=3.3 and g(−2)=7.2. Find the
equation for g.
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Points (1.1,3.3) and (-2,7.2);

You could start with point-slope form, and say g%28x%29-3.3=%28%287.2-3.3%29%2F%28-2-1.1%29%29%28x-1.1%29; continue from that.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
a linear function g%28x%29=ax%2Bb
given:
g%281.1%29=3.3 =>x=1.1,g%28x%29=3.3, that is a point (1.1,3.3)

g%28-2%29=7.2=>x=-2,g%28x%29=7.2 that is a point (-2,7.2)

use given points and set system of equations:

g%28x%29=ax%2Bb ....substitute x=1.1,g%28x%29=3.3
3.3=a%2A1.1%2Bb........solve for b
3.3-1.1a=b......eq.1

g%28x%29=ax%2Bb ....substitute x=-2,g%28x%29=7.2
7.2=-2a%2Bb
7.2%2B2a=b.....eq.2

equal the left sides of eq.1 and eq.2 and solve for a
3.3-1.1a=7.2%2B2a
3.3-7.2=1.1a%2B2a
-3.9=3.1a
a=-3.9%2F3.1
a=-1.258064516129
a=-1.3
go to eq.1 and substitute a
3.3-1.1%28-1.26%29=b......eq.1
3.3%2B1.386=b
b=4.686
b=4.7
and your equation is:

g%28x%29=-1.3x%2B4.7

check the graph: