Question

graph the line that passes through the points (0, -6) and (-6, -1) and determine the equation of the line.

Explanation:

Step1: Calculate the slope

The formula for slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Using points \( (0, -6) \) and \( (-6, -1) \), we have \( x_1 = 0, y_1 = -6, x_2 = -6, y_2 = -1 \). So \( m = \frac{-1 - (-6)}{-6 - 0} = \frac{5}{-6} = -\frac{5}{6} \).

Step2: Identify the y-intercept

The point \( (0, -6) \) is on the y-axis, so the y-intercept \( b = -6 \).

Step3: Write the equation

Using the slope-intercept form \( y = mx + b \), substitute \( m = -\frac{5}{6} \) and \( b = -6 \). The equation is \( y = -\frac{5}{6}x - 6 \).

Answer:

The equation of the line is \( y = -\frac{5}{6}x - 6 \) (To graph, plot the points \( (0, -6) \) and \( (-6, -1) \) and draw a straight line through them).