Question

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

Explanation:

Step1: Identify slope and intercept

Slope-intercept form: \( y = mx + b \), where \( b \) is y-intercept. From graph, line crosses y-axis at \( (0, 6) \), so \( b = 6 \). To find slope \( m \), use two points: \( (0, 6) \) and \( (2, 2) \). Slope formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 6}{2 - 0} = \frac{-4}{2} = -2 \).

Step2: Write the equation

Substitute \( m = -2 \) and \( b = 6 \) into \( y = mx + b \): \( y = -2x + 6 \).

Answer:

\( y = -2x + 6 \)