Question

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

Explanation:

Step1: Identify slope and intercept

Slope-intercept form is \( y = mx + b \), where \( m \) is slope and \( b \) is y-intercept. From the graph, the line crosses y-axis at \( (0, 6) \), so \( b = 6 \). To find slope, use two points, e.g., \( (0, 6) \) and \( (3, 5) \). Slope \( m=\frac{5 - 6}{3 - 0}=\frac{-1}{3}=-\frac{1}{3} \).

Step2: Write the equation

Substitute \( m = -\frac{1}{3} \) and \( b = 6 \) into \( y = mx + b \).
\( y = -\frac{1}{3}x + 6 \)

Answer:

\( y = -\frac{1}{3}x + 6 \)