Question

Explain how to write a function rule from the table below. Then write a function rule.

Answer 1

To find the slope you do y1-y2/x1-x2

To find the y intercept you look at when x is zero what is y.

Equation is y=-1/2x -2

Answer 2

Answer:

The required function is $y=\frac{-1}{2}x+2$                                    

Step-by-step explanation:

Given : Function table,

x 2 4 6

y 1 0 –1

To find : Explain how to write a function rule from the table and then write a function rule?

Solution :  

To determine the function is linear, quadratic or exponential we find the difference of y-values.

y from 1 to 0 is 1 and from 0 to -1 is 1.

So, the difference is same the function is linear.  

The general point slope form of linear equation is $y-y_1=m(x-x_1)$

m is the slope given as $m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{0-1}{4-2}$

$m=\frac{-1}{2}$

Substitute m and one point let (2,1) in general form.

$y-1=\frac{-1}{2}(x-2)$

$y-1=\frac{-1}{2}x+1$

$y=\frac{-1}{2}x+1+1$

$y=\frac{-1}{2}x+2$

Therefore, The required function is $y=\frac{-1}{2}x+2$