Explain how to write a function rule from the table below. Then write a function rule.
Table:
x: y:
2 1
4 0
6 -1
Please explain how to do this so I can do it on my own in the future.
Thanks.

Question

Explain how to write a function rule from the table below.  Then write a function rule.
Table:
x:     y:
2     1
4     0
6     -1
Please explain how to do this so I can do it on my own in the future.
Thanks.

imstuck · Answer

The first thing to do is to find the slope of the line using the points they provided.  The slope formula is the difference of the y points (y2 - y1) over the difference of the x points (x2 - x1), since slope is rise over run and rise is the y axis and run is the x axis.  I chose the two points (2, 1) and (4, 0).  The y2 - y1 would be 0 - 1, and the x2 - x1 would be 4 - 2.  0 - 1/4 - 2 = -1/2.  That's the slope of the line.  Now to get an equation or a function for this.  Use the point-slope format to do this part, which is$$y-y _{1}=m(x-x _{1})$$ where m is the slope you just found and y1 and x1 are coordinates from any ONE of the points given in the table.  Heres how it looks using point (4, 0):$$y - 0=-\frac{ 1 }{ 2 }(x-4)$$Now distribute the -1/2 into the parenthesis and get $$y-0=-\frac{ 1 }{ 2 }x+2$$ Move the zero over to the other side to set the whole thing to = y.  Most times this number will not be a zero, and moving it will affect the other side of the equation, but since it is zero, we get a final function or linear equation of$$y=-\frac{ 1 }{ 2 }x+2$$with your slope as -1/2 and your y-intercept as a positive 2.  Do you see that?

shiree19 · Answer

yes.  thanks.

shiree19 · Answer

But, I thought that a function rule was like:
f(x) = ..........
how does that factor in with this problem?