SOLUTION: Y = 3 what is the slope for this line?
X = -2 what is the slope for this line?
Are they perpendicular? Explain
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Question 250932: Y = 3 what is the slope for this line?
X = -2 what is the slope for this line?
Are they perpendicular? Explain
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the slope for y = 3 is 0.
the slope for x = -2 is undefined.
they are perpendicular to each other because the slope of 1 is a negative reciprocal of the other.
negative reciprocal of a slope is equal to -1 divided by the slope.
negative reciprocal of 0 is equal to -1/0 which is undefined.
since the slopes of the 2 lines follow the rules for being negative reciprocals of each other, then the lines are perpendicular to each other.
standard form of the equation of a line is ax + by = c
y = 3 converted to this form is equivalent to:
0*x + 1*y = 3
x = -2 converted to this form is equivalent to:
1*x + 0*y = -2
since the terms being multiplied by 0 cancel out, these equations become:
y = 3 and x = -2
the equations you are seeing are in standard form.
the slope intercept form of these equations is:
y = m*x + b where:
m is the slope.
b is the y-intercept.
we will convert the standard form of these equations to slope intercept form so show you what is happening with the slope.
we will take the original standard form before the canceling out of the terms.
they are:
0*x + 1*y = 3
1*x + 0*y = -2
to convert these, you solve for y in both equations.
the first equation is:
0*x + 1*y = 3
subtract 0*x from both sides of the equation to get:
1*y = -0*x + 3
divide both sides of this equation by 1 to get:
y = (-0/1)*x + (3/1)
this is in slope intercept form with m*x = (-0/1)*x, so the slope is equal to (-0/1) which is equivalent to 0.
y = 3 is equivalent to standard form of 0*x + 1*y = 3 which is equivalent to slope intercept form of y = 0*x + 3 with a slope of 0.
the second equation is:
1*x + 0*y = -2
subtract 1*x from both sides of this equation to get:
0*y = -1*x - 2
divide both sides of this equation by 0 to get:
y = (-1/0)*x - (2/0)
this is in slope intercept form with m*x = (-1/0)*x, so the slope is equal to (-1/0) which is undefined.
x = -2 is equivalent to standard form of 1*x + 0*y = -2 which is equivalent to slope intercept form of y = (-1/0)*x - (2/0) with a slope that is undefined.
note that the y-intercept is equal to (2/0) which is also undefined.
a slope of (-1/0) is the negative reciprocal of a slope of 0 meaning that y = 3 and x = -2 are perpendicular to each other.
y = 3 is a horizontal line 3 units above the x-axis.
x = -2 is a vertical line 2 units to the left of the y-axis.
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