Which is the equation of the line with slope 0 passing through the point $(-3,-1)$?
A. $x=-3$
B. $y=-3$
C. $x=-1$
D. $y=-1$
Answer (2)
The line has a slope of 0 and passes through the point ( − 3 , − 1 ) .
Using the point-slope form of a line: y − y 1 = m ( x − x 1 ) .
Substituting the given values: y − ( − 1 ) = 0 ( x − ( − 3 )) .
Simplifying the equation gives the equation of the line: y = − 1 .
Explanation
Understanding the Problem We are given a line with a slope of 0 that passes through the point ( − 3 , − 1 ) . Our goal is to find the equation of this line.
Using Point-Slope Form The point-slope form of a line is given by the equation: y − y 1 = m ( x − x 1 ) where m is the slope of the line and ( x 1 , y 1 ) is a point on the line.
Substituting Values We are given that the slope m = 0 and the point is ( − 3 , − 1 ) . Substituting these values into the point-slope form, we get: y − ( − 1 ) = 0 ( x − ( − 3 ))
Simplifying the Equation Simplifying the equation, we have: y + 1 = 0 ( x + 3 ) y + 1 = 0 y = − 1
Final Answer Therefore, the equation of the line is y = − 1 .
Examples
Imagine you're walking on a perfectly flat ground. The slope is 0 because you're not going uphill or downhill. If you mark a point on the ground, say at a height of -1 meter (perhaps you're in a slight depression), and you continue walking on the flat ground, your height will always be -1 meter. The equation y = − 1 represents this flat path.
The equation of the line with a slope of 0 passing through the point ( − 3 , − 1 ) is y = − 1 . Therefore, the answer is option D: y = − 1 .
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