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 \( (0, -7) \), so \( b = -7 \). To find slope \( m \), use two points, e.g., \( (0, -7) \) and \( (1, -8) \). Slope formula: \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-8 - (-7)}{1 - 0}=\frac{-1}{1}=-1 \).

Step2: Write the equation

Substitute \( m = -1 \) and \( b = -7 \) into \( y = mx + b \): \( y=-1x - 7 \) or \( y = -x - 7 \).

Answer:

\( y = -x - 7 \)