Question

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

Explanation:

Step1: Identify slope-intercept form

Slope-intercept form is \( y = mx + b \), where \( m \) is slope and \( b \) is y-intercept. From the graph, the line crosses the y-axis at \( (0, 2) \), so \( b = 2 \).

Step2: Calculate the slope \( m \)

Use two points, e.g., \( (0, 2) \) and \( (5, -3) \). Slope formula: \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-3 - 2}{5 - 0}=\frac{-5}{5}=-1 \).

Step3: Write the equation

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

Answer:

\( y = -x + 2 \)