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For example, the line #y=3x# has a slope of 3. Any line that is perpendicular to it must be opposite (negative instead of positive or vice versa) reciprocals (multiplicative inverse, reciprocals multiply to 1, flip the numerator and denominator) Opposite of 3: -3. Reciprocal of -3 (#-3/1#): #-1/3#
The perpendicular slope m=1/4 The perpendicular slope to any given line is the inverse reciprocal of the slope. Given the original slope of m=-4 or m=-4/1 We can take the inverse and the reciprocal which makes the perpendicular slope m=1/4
0 Compare to: The slope for x=2 is a vertical line perpendicular to the x-axis but crossing the x-axis at x=2 So the slope x=0 is vertical to the axis but crossing it at x=0. In other words it is the y-axis. Slope (gradient) is the amount of up for the amount of along -> (y_2 - y_1)/(x_2-x_1) The slope for x=0 can not be quantitised as you are unable to have different values for x_1 "and x_2 ...
2/3 Perpendicular slopes are opposite reciprocals of one another. Opposites: put a negative sign in front of one number to find its opposite Examples: 6 rarr -6 -2/3 rarr -(-2/3) rarr 2/3 Thus, the opposite of -3/2 is 3/2 Reciprocals: flip the numerator and denominator of the number to find its reciprocal Examples: -5 rarr (-5)/1 rarr 1/(-5) rarr -1/5 3/4 rarr 4/3 The reciprocal of 3/2 is 2/3
The slope of a line perpendicular to a line with a slope of #0# is undefined. The perpendicular line is a vertical line. A line with a slope of #0# is a horizontal line. A vertical line would be perpendicular to the horizontal line, but the slope of a vertical line is undefined. For example:
The parallel is 7/3 The negative inverse of 7/3 is the perpendicular slope. Lines that are parallel have the same slope. Lines that are perpendicular are negative inverses of each other so 7/3 xx - 3/7 = -1 and you can find this by dividing -1 by 7/3 and -1-:7/3=-1xx3/7=-3/7 So the slope of the perpendicular any where along the line is -3/7
The slope that is perpendicular to #3/4# is its negative reciprocal, which is #-4/3#. Mathematically. #m_1m_2=-1#, where #m_1# is the given slope and #m_2# is the perpendicular slope. #3/4m_2=-1# Multiply both sides by #4/3#.
The perpendicular slope of any original slope is derived by negating the original slope and then "flipping" the fraction. By "flipping" the fraction, I mean find the inverse of the original slope. So for example: Original slope: #m_("orig")=-1/5# Step 1. Negate the original slope. Remember that a negative of a negative is a positive. #-(-1/5)=1 ...
-3 Perpendicular slopes are opposite reciprocals of each other. Opposites: positive vs negative The perpendicular slope of a positive slope must be negative, and vice versa. Reciprocals: multiplicative inverses (the numbers will multiply to 1) Examples of reciprocals: 2, 1/2 rarr 2*1/2=1 1/3, 3 rarr 1/3*3=1 The opposite of 1/3 is -1/3, the reciprocal of -1/3 is -3.
The slope of a line perpendicular to a line with slope m is -1/m. The line we are looking for, therefore, has a slope of 3/5. Standard form of a line is: y=mx+b where m is the slope and b is the y-intercept. For another line perpendicular, the slope will be -1/m. In this case, that is -1/(-5/3) = 3/5.