Question

look at this table:

x	y
-5	7
-4	6
-3	5
-2	4
-1	3

write a linear ($y = mx + b$), quadratic ($y = ax^2$), or exponential ($y = a(b)^x$) function that models the data.
$y = \boxed{}$

Explanation:

Step1: Check linearity (constant slope)

Calculate the slope between consecutive points:
$\text{Slope } m = \frac{\Delta y}{\Delta x} = \frac{6-7}{-4-(-5)} = \frac{-1}{1} = -1$
$\frac{5-6}{-3-(-4)} = \frac{-1}{1} = -1$, $\frac{4-5}{-2-(-3)} = -1$, $\frac{3-4}{-1-(-2)} = -1$

Step2: Find y-intercept $b$

Use point $(-1, 3)$ and $m=-1$ in $y=mx+b$:
$3 = (-1)(-1) + b$
$3 = 1 + b$
$b = 3 - 1 = 2$

Step3: Form the linear function

Substitute $m=-1$ and $b=2$ into $y=mx+b$
$y = -x + 2$

Answer:

$y = -x + 2$