Question

write the equation of this line in slope-intercept form.

Explanation:

Step1: Recall slope-intercept form

Slope-intercept form is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Step2: Find the y-intercept (\( b \))

The line crosses the y-axis at \( (0, -2) \), so \( b = -2 \).

Step3: Calculate the slope (\( m \))

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

Step4: Write the equation

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

Answer:

\( y = x - 2 \)