Question

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write the equation of the line in fully simplified slope - intercept form.

Explanation:

Step1: Find the slope ($m$)

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Using the points $(0,6)$ (y - intercept, so $x_1 = 0,y_1=6$) and $(6,0)$ ($x_2 = 6,y_2 = 0$).
$m=\frac{0 - 6}{6-0}=\frac{-6}{6}=- 1$.

Step2: Use the slope - intercept form ($y=mx + b$)

The slope - intercept form is $y = mx + b$, where $b$ is the y - intercept.
From the graph, the y - intercept $b = 6$ and $m=-1$.
Substitute $m$ and $b$ into the formula: $y=-1x + 6$.

Answer:

$y=-x + 6$