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How Do You Find the Slope of a Line If You Have a Perpendicular Line?

Find the slope of the line (in slope-intercept form) that is perpendicular to the graph of 2x-y = 2

Summary

  1. 'L1' is a variable representing our given line
  2. 'L2' is a variable representing the parallel line we are trying to find
  3. 'y=mx+b' is the form of an equation in slope-intercept form, where 'm' is the slope and 'b' is the intercept
  4. '2x-y=2' is our given equation, written in standard form
  5. 'y=2x-2' is our given equation, rewritten in slope-intercept form
  6. The product of two perpendicular lines' slopes is '-1'
  7. So the slope of 'L2' is '-1/2'

Notes

    1. 'L1' is a variable representing the line given to us
    2. 'L2' is a variable representing the line perpendicular to 'L1'
    3. We are trying to figure out the equation of 'L2'
    1. The first step in trying to find the equation of 'L2' is finding the slope
    1. Remember, parallel lines have the exact same slope
    2. The slopes of perpendicular lines also have a relationship
    1. '2x-y=2' is the line we were given, which is in standard form
    1. '2x-y=2' is the line we were given, which is in standard form
    1. '2x-y=2' is the line we were given, which is in standard form
    2. 'y=mx+b' is the form for an equation in slope-intercept form, where 'm' is the slope and 'b' is the intercept
    1. '2x-y=2' is the line we were given, which is in standard form
    2. 'y=mx+b' is the form for an equation in slope-intercept form, where 'm' is the slope and 'b' is the intercept
    3. Remember, we want to know the slope of our given line since it is related to the slope of the perpendicular line
    1. '2x-y=2' is the line we were given, which is in standard form
    2. 'y=mx+b' is the form for an equation in slope-intercept form, where 'm' is the slope and 'b' is the intercept
    3. Remember, we want to know the slope of our given line since it is related to the slope of the perpendicular line
    1. '2x-y=2' is the line we were given, which is in standard form
    2. 'y=mx+b' is the form for an equation in slope-intercept form, where 'm' is the slope and 'b' is the intercept
    3. Remember, we want to know the slope of our given line since it is related to the slope of the perpendicular line
    1. '2x-y=2' is the line we were given, which is in standard form
    2. 'y=mx+b' is the form for an equation in slope-intercept form, where 'm' is the slope and 'b' is the intercept
    3. Remember, we want to know the slope of our given line since it is related to the slope of the perpendicular line
    4. When we multiply by -1, all signs flip
    1. '2x-y=2' is the line we were given, which is in standard form
    2. 'y=mx+b' is the form for an equation in slope-intercept form, where 'm' is the slope and 'b' is the intercept
    3. 'y=2x-2' is now our rearranged equation for the given line
    1. '2x-y=2' is the line we were given, which is in standard form
    2. 'y=mx+b' is the form for an equation in slope-intercept form, where 'm' is the slope and 'b' is the intercept
    3. 'y=2x-2' is now our rearranged equation for the given line
    1. '2x-y=2' is the line we were given, which is in standard form
    2. 'y=mx+b' is the form for an equation in slope-intercept form, where 'm' is the slope and 'b' is the intercept
    3. 'y=2x-2' is now our rearranged equation for the given line
    4. Remember, we want to know the slope of our given line since it is related to the slope of the perpendicular line
    1. 'y=mx+b' is the form for an equation in slope-intercept form, where 'm' is the slope and 'b' is the intercept
    2. 'y=2x-2' is our rearranged equation for the given line
    3. Remember, we want to know the slope of our given line since it is related to the slope of the perpendicular line
    1. 'y=mx+b' is the form for an equation in slope-intercept form, where 'm' is the slope and 'b' is the intercept
    2. 'y=2x-2' is our rearranged equation for the given line
    3. Remember, we want to know the slope of our given line since it is related to the slope of the perpendicular line
    1. 'y=mx+b' is the form for an equation in slope-intercept form, where 'm' is the slope and 'b' is the intercept
    2. 'y=2x-2' is our rearranged equation for the given line
    3. Remember, we want to know the slope of our given line since it is related to the slope of the perpendicular line
    4. The slope, or 'm', in our rearranged equation is '2'
    1. Remember, the slope of our given line is related to the slope of the perpendicular line
    1. Remember, the slope of our given line is related to the slope of the perpendicular line
    1. Remember, the slope of our given line is related to the slope of the perpendicular line
    2. The relationship is:
    3. 'L2•1=-1'
    1. Remember, the slope of our given line is related to the slope of the perpendicular line
    2. The relationship is:
    3. 'L2•1=-1'
    4. We just found that '2' is the slope of our given line, 'L1'
    1. Remember, the slope of our given line is related to the slope of the perpendicular line
    2. The relationship is:
    3. 'L2•1=-1'
    4. We just found that '2' is the slope of our given line, 'L1'
    5. So 'L2•1=-1' becomes 'L2•2=-1'
    1. Up to this point, 'L2•2=-1' is our equation to find the slope of 'L2
    2. Dividing both sides by 2 gives us the slope of 'L2' alone on the left, and shows us that it's equal to '-1/2'
    1. The slope of 'L2' is equal to '-1/2'
    2. Remember, the slope of 'L1' is '2'
    1. The slope of 'L2' is equal to '-1/2'
    2. Remember, the slope of 'L1' is '2'
    1. The slope of 'L2' is equal to '-1/2'
    2. Remember, the slope of 'L1' is '2'
    3. The slope of 'L1' is related to the slope of 'L2', and there is a quick way to find the slope of one if you know the slope of the other
    1. The slope of 'L2' is equal to '-1/2'
    2. Remember, the slope of 'L1' is '2'
    3. The slope of 'L1' is related to the slope of 'L2', and there is a quick way to find the slope of one if you know the slope of the other
    4. The negative slope of 'L1' is '-2'
    1. The slope of 'L2' is equal to '-1/2'
    2. Remember, the slope of 'L1' is '2'
    3. The slope of 'L1' is related to the slope of 'L2', and there is a quick way to find it
    4. The negative slope of 'L1' is '-2'
    5. Since '-2' is the same as '-2/1', it's reciprocal is '-1/2'
    1. Remember, '-2' in fraction form is '-2/1'
    2. Since '-2' is the same as '-2/1', it's reciprocal is '-1/2'
    1. '2' is a whole number
    2. Since '-2' is the same as '-2/1', it's reciprocal is '-1/2'
    1. The known slope was '2'
    2. The negative reciprocal of '2' is '-1/2'