Graphing a functions using a verbal description.

Question

A linear function h models a relationship in which the dependent variable increases 1 unit for every 5 units the independent variable decreases. The value of the function at 0 is 3. 

Answer 1

Recognize that the problem is describing the components of the 

"slope-intercept" form (y=mx+b) of a linear equation.  It describes...

 

1.  "...increases 1 unit for every 5 units...decreases" describes

slope, "m" ("rise over run"). Increase is a positive value (up,

dependent value "y") and decrease is a negative value (left,

independent value "x").  So we have...

 

         m=1/-5=-(1/5)

 

2.  "...value of the function at 0 is 3" describes the y-intercept, "b",

          or coordinate (0,3).

 

         b=3

 

Let's substitute these values into the slope-intercept form of 

the linear equation...

 

         y=-(1/5)x+3......Eq1, slope-intercep form of linear

                                  equation.

 

Let's check our solution by plugging in the point (0,3) from

the problem statement into Eq1...

 

    3=-(1/5)(0)+3...substitute "0 for x" and "3 for y".

    3=0+3..............simplify

    3=3..................true, √check, our solution equation is correct.

 

Always check your solution and work!

 

So our solution equation rewritten in function notation reads...

     h(x)=(-1/5)x+3