Question 1093038: Find the equation of the line through the point (-4,-5) and perpendicular to y=-1.
Thank you!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! y = -1 is a horizontal line.
a line perpendicular to a horizontal line is a vertical line.
a vertical line that goes through the point (-4,-5) is x = -4
the intersection of the two lines will be (-4,-1).
here's a graph of both lines.
the line y = -1 is red.
the line x = -4 is blue.
the line y = -5 is green.
it is drawn there to show you that the point (-4,-5) is also on the line x = -4.
in fact, the line y = -1 contains all values of x at y = -1 and the line x = -4 contains all values of y at x = -4.
the coordinate points on the line y = -1 is (x,-1) where the x-coordinate can be any real number and the y-coordinate is always equal to -1.
the coordinate points on the line x = -4 is (-4,y) where the x-coordinate is always equal to -4 and the y-coordinate can be any real number.
the standard form of a straight line is ax + by = c, where a is the coefficient of the x term and y is the coefficient of the y term and c is the constant term.
when the line is vertical, the coefficient of the y term is equal to 0 and you get ax + 0y = c which then becomes ax = c.
when you solve for x, you get x = c/a.
when the line is horizontal, the coefficient of the x term is equal to 0 and you get 0x + by = c which then becomes by = c
when you solve for c, you get y = c/b.
the slope intercept form of a straight line is y = mx + b where m is the slope and b is the y-intercept.
the slope of a horizontal line is equal to 0.
the slope of a vertical line is undefined.
short answer to your question:
the equation of the line perpendicular to y = -1 going through the point (-4,-5) is x = -4.
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