Question

HURRY! Which table represents a linear function?

Answer 1

Remember that to tell if a function is linear for a table, you should look for a constant rate of change, and the only function that has a constant rate of change is the first one. $x$ is increasing by 1, and $y$ is increasing by 0.5.

Now that we know that, lets find the equation of our table.
First, lets take tow points from our table: (1,$\frac{1}{2}$) and $(2,1)$.
Next, use the slope formula: $m= \frac{y_{2}-y_{1}}{x_{2}-x_{1} }$ 
We know for our points that $y_{2}=1$, $y_{1}= \frac{1}{2}$,$x_{2}=2$, and $x_{1}=1$, so lets replace those point in our formula to find $m$:
$m= \frac{1- \frac{1}{2} }{2-1}$
$m= \frac{1}{2}$

Finally, we can use the point slope formula $y-y_{1}=m(x-x_{1})$ to find our equation:
$y- \frac{1}{2} = \frac{1}{2} (x-1)$
$y- \frac{1}{2} = \frac{1}{2} x- \frac{1}{2}$
$y= \frac{1}{2}x$

We can conclude that the first table represents a linear function, and its equation is $y= \frac{1}{2}x$