Question

given the table below, write a linear equation that defines the dependent variable, y, in terms of the independent variable, x.

x	y
1	10
2	8
3	6

show your work here

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using the points (0, 12) and (1, 10):
$m = \frac{10 - 12}{1 - 0} = \frac{-2}{1} = -2$

Step2: Identify the y-intercept (b)

When $x = 0$, $y = 12$, so the y-intercept $b = 12$.

Step3: Write the linear equation

The slope-intercept form of a linear equation is $y = mx + b$. Substituting $m = -2$ and $b = 12$:
$y = -2x + 12$

Answer:

$y = -2x + 12$