12. write an equation for line that best fits the graph.

Explanation:

Step1: Identify the y-intercept

The line of best fit crosses the y-axis at $(0, 5)$. $$b = 5$$

Step2: Identify a second point

The line passes through the x-axis at approximately $(5, 0)$. $$(x_1, y_1) = (0, 5), (x_2, y_2) = (5, 0)$$

Step3: Calculate the slope

Use the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. $$m = \frac{0 - 5}{5 - 0} = \frac{-5}{5} = -1$$

Step4: Write the equation

Substitute $m$ and $b$ into the slope-intercept form $y = mx + b$. $$y = -1x + 5$$

Answer:

$y = -x + 5$