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 \( (0, -8) \), so \( b = -8 \). To find slope \( m \), use two points, e.g., \( (0, -8) \) and \( (2, -9) \). Slope formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-9 - (-8)}{2 - 0} = \frac{-1}{2} \).

Step2: Write the equation

Substitute \( m = -\frac{1}{2} \) and \( b = -8 \) into \( y = mx + b \): \( y = -\frac{1}{2}x - 8 \).

Answer:

\( y = -\frac{1}{2}x - 8 \)