Question

write the equation of the line in fully simplified slope-intercept form.
answer attempt 1 out of 2

Explanation:

Step1: Identify slope-intercept form

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

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

The line crosses the y-axis at \( (0, -6) \), so \( b = -6 \).

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

Use two points, e.g., \( (0, -6) \) and \( (6, 0) \). Slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-6)}{6 - 0} = \frac{6}{6} = 1 \).

Step4: Write the equation

Substitute \( m = 1 \) and \( b = -6 \) into \( y = mx + b \): \( y = x - 6 \).

Answer:

\( y = x - 6 \)