Question

write a linear function f with the given values.

x	f(x)
-4	-2
-2	-1
0	0

f(x) =

Explanation:

Step1: Find the slope

The slope $m$ of a linear - function $y = mx + b$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(x_1,y_1)=(-4,-2)$ and $(x_2,y_2)=(-2,-1)$, we have $m=\frac{-1-(-2)}{-2-(-4)}=\frac{-1 + 2}{-2 + 4}=\frac{1}{2}$.

Step2: Find the y - intercept

The y - intercept $b$ is the value of $y$ when $x = 0$. From the table, when $x = 0$, $y = 0$, so $b = 0$.

Step3: Write the linear function

The linear function in slope - intercept form is $y=mx + b$. Substituting $m=\frac{1}{2}$ and $b = 0$ into the equation, we get $f(x)=\frac{1}{2}x$.

Answer:

$\frac{1}{2}x$