To find the equation of the line that contains the given point and has the given slope, we need to follow these steps:
1. Identify the slope: We are given that the slope [tex]\( m = 0 \)[/tex].
2. Understand the meaning of the slope: A slope of zero means that the line is horizontal. For a horizontal line, the value of [tex]\( y \)[/tex] remains constant at any point on the line.
3. Use the given point: We are given the point [tex]\( (5, 6) \)[/tex]. For a horizontal line, since the slope ([tex]\( m \)[/tex]) is zero, the equation will be of the form [tex]\( y = \text{constant} \)[/tex].
4. Determine the constant value: Since the line passes through the point [tex]\( (5, 6) \)[/tex], we set [tex]\( y \)[/tex] equal to 6 (the y-coordinate of the given point).
Therefore, the equation of the line is [tex]\( y = 6 \)[/tex].
Given the choices:
a) [tex]\( y = 6 \)[/tex]
b) [tex]\( x = 6 \)[/tex]
c) [tex]\( y = 5x + 6 \)[/tex]
d) [tex]\( y = x + 6 \)[/tex]
The correct choice is (a) [tex]\( y = 6 \)[/tex].
