Question

look at this table:

x	y
-2	-5
-1	-6
0	-7
1	-8
2	-9

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

Explanation:

Step1: Check linearity (constant Δy)

Calculate change in y:
$\Delta y_1 = -6 - (-5) = -1$
$\Delta y_2 = -7 - (-6) = -1$
$\Delta y_3 = -8 - (-7) = -1$
$\Delta y_4 = -9 - (-8) = -1$

Step2: Find slope m

Slope $m = \frac{\Delta y}{\Delta x} = \frac{-1}{1} = -1$

Step3: Find y-intercept b

Use x=0, y=-7: $b = -7$

Step4: Build linear equation

Substitute m and b into $y=mx+b$

Answer:

$y = -x - 7$