www.VirtualNerd.com

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

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

Summary

  1. Our first step is to graph the line of our equation 'y=2x-2' on a coordinate plane
  2. The y-intercept of our line is '-2', so the line must pass through the point (0,-2)
  3. Since the slope, 'm', is '2', we can plot a second point up 2 and to the right 1
  4. We can repeat this process of plotting points since the slope is constant
  5. Connecting the dots will give us the graphed line of our equation
  6. Looking at the graphed line, we see that the point (3,4) does lie on the our line!

Notes

    1. The equation 'y=2x-2' is in slope-intercept form, which will make it easier to graph
    2. Slope-intercept form is:
    3. y=mx+b
    1. An x and y-coordinate axis make up what is called a coordinate plane
    2. We can graph our line 'y=2x-2' on this coordinate plane
    1. Slope-intercept form is:
    2. y=mx+b
    1. Slope-intercept form is:
    2. y=mx+b
    3. The y-intercept, 'b', is where the line of our equation passes through the y-axis
    4. Our equation is 'y=2x-2'
    5. Since '-2' is our y-intercept, we know (0,-2) falls on the line of our equation
    6. So (0,-2) is the first point we plot
    1. Our equation is 'y=2x-2', so the y-intercept, 'b', is '-2', and the slope, 'm', is '2'
    2. (0,-2) is the first point we plotted
    1. Our equation is 'y=2x-2', so the y-intercept, 'b', is '-2', and the slope, 'm', is '2'
    2. (0,-2) is the first point we plotted
    3. A slope of '2' is the same as a slope of '2 over 1', which means we can keep plotting points up 2 and right 1
    1. The dots represent the points: (0,-2), (1,0), (2,2), (3,4)
    2. Connecting the dots gives us the line of our equation 'y=2x-2'
    1. The dots represent the points: (0,-2), (1,0), (2,2), (3,4)
    2. Connecting the dots gives us the line of our equation 'y=2x-2'
    1. (3,4) means the x-coordinate will be '3' and the y-coordinate will be '4'
    1. (3,4) means the x-coordinate will be '3' and the y-coordinate will be '4'
    1. (3,4) means the x-coordinate will be '3' and the y-coordinate will be '4'
    1. (3,4) means the x-coordinate will be '3' and the y-coordinate will be '4'
    2. So (3,4) DOES lie on the line with the equation 'y=2x-2'
    1. We know this just by looking at the graph itself
    2. Drawing the line correctly is key to this problem!