Question

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

x	y
2	-7
3	-8
4	-9

Explanation:

Step1: Calculate the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using the points (1, -6) and (2, -7):
$m = \frac{-7 - (-6)}{2 - 1} = \frac{-1}{1} = -1$

Step2: Find the y-intercept (b)

Use the slope-intercept form $y = mx + b$ and substitute $m = -1$ and a point (e.g., (1, -6)):
$-6 = -1(1) + b$
$-6 = -1 + b$
$b = -6 + 1 = -5$

Step3: Write the equation

Substitute $m = -1$ and $b = -5$ into $y = mx + b$:
$y = -x - 5$

Answer:

$y = -x - 5$