What is the equation of the line that passes through $(0,2)$ and has a slope of $0$?
A. $y=2$
B. $x=2$
C. $y=-2$
Answer (1)
Use the point-slope form of a linear equation: y − y 1 = m ( x − x 1 ) .
Substitute the given point ( 0 , 2 ) and slope 0 into the point-slope form: y − 2 = 0 ( x − 0 ) .
Simplify the equation: y = 2 .
The equation of the line is y = 2 .
Explanation
Understanding the Problem We are given a point ( 0 , 2 ) and a slope m = 0 . We want to find the equation of the line that passes through this point and has this slope.
Using Point-Slope Form The point-slope form of a linear equation is given by: y − y 1 = m ( x − x 1 ) where ( x 1 , y 1 ) is a point on the line and m is the slope of the line.
Substituting Values and Simplifying We are given the point ( 0 , 2 ) , so x 1 = 0 and y 1 = 2 . We are also given the slope m = 0 . Substituting these values into the point-slope form, we get: y − 2 = 0 ( x − 0 ) y − 2 = 0 y = 2
Finding the Equation of the Line The equation of the line is y = 2 .
Examples
Imagine you're walking on a perfectly flat road. The road represents a line with a slope of 0. If you start at a height of 2 meters (the point (0,2)), no matter how far you walk horizontally, your height will always remain 2 meters. This horizontal line at a constant height is described by the equation y = 2 . Understanding such lines is crucial in various fields like physics, where it can represent constant velocity or potential energy.
