Question

find the equation of the linear function represented by the table below in slope-intercept form.

x	y
2	-6
3	-7
4	-8

Explanation:

Step1: Calculate the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using the points (1, -5) and (2, -6):
$m = \frac{-6 - (-5)}{2 - 1} = \frac{-1}{1} = -1$

Step2: Find the y-intercept (b)

Use the slope-intercept form $y = mx + b$ and substitute $m = -1$ and a point (e.g., (1, -5)):
$-5 = -1(1) + b$
$-5 = -1 + b$
Add 1 to both sides: $b = -5 + 1 = -4$

Step3: Write the equation

Substitute $m = -1$ and $b = -4$ into $y = mx + b$:
$y = -x - 4$

Answer:

$y = -x - 4$