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How Do You Write an Equation of a Line in Slope-Intercept Form If You Have One Point and a Perpendicular Line?

Find an equation of the line (in slope-intercept form) that passes through (1,10) and is perpendicular to the graph of 2x-y=2.

Summary

  1. Whenever we refer to L1, we mean 2x-y=2 in any of it's forms
  2. The slope of L1 is 2!
  3. For slope-intercept form, m is the slope and b is the y-intercept
  4. L2 stands for the line we're trying to find
  5. After plugging the slope and our point into L2 we can solve the equation for the y-intercept

Notes

    1. Opposite numbers have the same absolute value but with different signs
    1. Product means multiplication
    2. Numbers that are reciprocals of each other always have a product of 1
    3. Opposite numbers have different signs, so their product is always negative
    1. Whenever we refer to L1, we mean 2x-y=2 in any of it's forms
    1. By L1 we mean 2x-y=2 in any of it's forms
    1. By L1 we mean 2x-y=2 in any of it's forms
    1. Move the y over to the right hand side by subtracting y from both sides
    2. Then move the 2 over to the left hand side by subtracting 2 from both sides
    3. Flip the equation over and the line is in slope-intercept form!
    1. Opposite numbers have the same absolute value but with different signs
    1. Opposite numbers have different signs, so their product is always negative
    2. Numbers that are reciprocals of each other always have a product of 1
    1. The slope of L1 is 2
    1. Divide by 2 on both sides to get the L2 slope by itself
    1. L2 represents the line we're trying to find
    1. L2 represents the line we're trying to find
    1. The y-intercept is where the line crosses the y-axis
    1. We can plug the slope in for m in our line y=mx+b
    1. We need the only variables in our equation to be x and y
    2. Since we still have b that we don't know, we're not done
    1. Since (1,10) is an x-y ordered pair, we can plug 1 in for x and 10 in for y
    1. Remember, b is the y-intercept of our line
    1. Since (1,10) is an x-y ordered pair, we can plug 1 in for x and 10 in for y
    1. Add 1/2 to both sides
    2. 10 is the same as 20/2, so 20/2 + 1/2 = 21/2
    1. We want to plug our value for b into L2
    1. This is the L2 equation
    1. L2 is the equation we just found, y=(-1/2)x+(21/2)