Question

question graph the line that passes through the points (-5, 6) and (8, 6) and determine the equation of the line.

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, \((x_1,y_1)=(-5,6)\) and \((x_2,y_2)=(8,6)\). So, \( m=\frac{6 - 6}{8 - (-5)}=\frac{0}{13}=0 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((-5,6)\) and \( m = 0 \), we get \( y - 6=0\times(x - (-5)) \), which simplifies to \( y-6 = 0 \), or \( y = 6 \).

Answer:

The equation of the line is \( y = 6 \)