Question

what is the equation of the line of best fit.
options:
\\( y= -3/9 x + 7 \\)
\\( y= 1/2 x - 7 \\)
\\( y= -3/ x + 7 \\) (note: likely a typo, maybe -3/6 or similar, but ocr as is)
\\( y= -1/2 x + 7 \\)

Explanation:

Step1: Identify the slope direction

The line of best fit is decreasing, so the slope \( m \) should be negative. This eliminates the option with positive slope (\( y = \frac{1}{2}x - 7 \)).

Step2: Find the y-intercept

The line crosses the y-axis at \( (0, 7) \), so the y-intercept \( b = 7 \).

Step3: Calculate the slope

Use two points on the line, e.g., \( (0, 7) \) and \( (6, 4) \). The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
Substituting values: \( m = \frac{4 - 7}{6 - 0} = \frac{-3}{6} = -\frac{1}{2} \).

Step4: Form the equation

Using slope-intercept form \( y = mx + b \), with \( m = -\frac{1}{2} \) and \( b = 7 \), the equation is \( y = -\frac{1}{2}x + 7 \).

Answer:

\( y = -\frac{1}{2}x + 7 \) (the last option: \( y = -1/2 x + 7 \))