Question

what is an equation of the line that passes through the points (0, -6) and (-5, -2)?

Explanation:

Step1: Calculate the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \((x_1, y_1)=(0, -6)\) and \((x_2, y_2)=(-5, -2)\). So, \(m=\frac{-2 - (-6)}{-5 - 0}=\frac{-2 + 6}{-5}=\frac{4}{-5}=-\frac{4}{5}\).

Step2: Use the slope-intercept form (\(y = mx + b\))

We know the y - intercept (b) because when \(x = 0\), \(y=-6\), so \(b=-6\). Now substitute \(m = -\frac{4}{5}\) and \(b=-6\) into \(y = mx + b\). We get \(y=-\frac{4}{5}x-6\).

Answer:

\(y = -\frac{4}{5}x - 6\)