Question

what is an equation of the line that passes through the points (-4, -6) and (8, -6)?

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1,y_1)=(-4,-6)\) and \((x_2,y_2)=(8,-6)\). So \( m=\frac{-6-(-6)}{8 - (-4)}=\frac{0}{12} = 0 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((-4,-6)\) and \( m = 0 \), we get \( y-(-6)=0\times(x - (-4)) \), which simplifies to \( y + 6=0 \), or \( y=-6 \).

Answer:

\( y=-6 \)