Question

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

x	y
2	-5
3	-7
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, -3) and (2, -5):
$m = \frac{-5 - (-3)}{2 - 1} = \frac{-2}{1} = -2$

Step2: Find the y-intercept (b)

Use the slope-intercept form $y = mx + b$ and substitute $m = -2$ and a point (e.g., (1, -3)):
$-3 = -2(1) + b$
$-3 = -2 + b$
Add 2 to both sides: $b = -3 + 2 = -1$

Step3: Write the equation

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

Answer:

$y = -2x - 1$