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How Do You Check if a Point is on a Line If You Have an Equation?

Verify that the point (3,4) lies on the line with equation y=2x-2

Summary

  1. Writing out the equation of our line, we see that we need values for 'x' and 'y'
  2. We plug the x and y coordinates from our point, (3,4), in for the 'x' and 'y' in our equation
  3. 2(3)=6
  4. 6-2=4
  5. '4=4' is a true statement, so (3,4) DOES lie on the line with the equation 'y=2x-2'

Notes

    1. Here, 'y=2x-2' is the equation of a line in slope-intercept form
    1. Our equation is 'y=2x-2'
    2. Since (3,4) is our point, we can plug it into our equation
    3. The x-coordinate of (3,4) is '3', and the y-coordinate is '4'
    1. Our equation is 'y=2x-2'
    2. Since (3,4) is our point, we can plug it into our equation
    3. The x-coordinate of (3,4) is '3', and the y-coordinate is '4'
    4. A true statement is when the values on both sides of the equal sign are the same
    1. Our equation is 'y=2x-2'
    2. Since (3,4) is our point, we can plug it into our equation
    3. The x-coordinate of (3,4) is '3', and the y-coordinate is '4'
    4. A true statement is when the values on both sides of the equal sign are the same
    1. Our equation is 'y=2x-2'
    2. Since (3,4) is our point, we can plug it into our equation
    3. The x-coordinate of (3,4) is '3', and the y-coordinate is '4'
    1. Our equation is 'y=2x-2'
    2. Since (3,4) is our point, we can plug it into our equation
    3. The x-coordinate of (3,4) is '3', and the y-coordinate is '4'
    4. After plugging in our point, 'y=2x-2' becomes '4=2(3)-2'
    1. Our equation is 'y=2x-2'
    2. Since (3,4) is our point, we can plug it into our equation
    3. The x-coordinate of (3,4) is '3', and the y-coordinate is '4'
    4. After plugging in our point, 'y=2x-2' becomes '4=2(3)-2'
    5. 2(3)=6
    1. Our equation is 'y=2x-2'
    2. Since (3,4) is our point, we can plug it into our equation
    3. The x-coordinate of (3,4) is '3', and the y-coordinate is '4'
    4. After plugging in our point, 'y=2x-2' becomes '4=2(3)-2'
    5. 2(3)=6
    6. 6-2=4
    7. '4=4' is a true statement!
    1. '4=4' is a true statement, so our point (3,4) does lie on the line!