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How Do You Find the Y-Coordinate of a Point on a Line If You Have a Graph?

Use the graph of y = 2x-2 to find y(4).

Summary

  1. Our first step is to graph the line of our equation 'y=2x-2' on a coordinate plane
  2. The y-intercept is -2, so we know the point (0,-2) will be on our line
  3. The slope is 2, or 2 over 1, so we can plot a point that is up 2 and right 1 of (0,-2)
  4. We can keep plotting points 2 up and 1 right of each other
  5. Connect the dots to graph the line with the equation 'y=2x-2'
  6. Since we're looking for 'y' when 'x' is '4', graph a dashed vertical line through 'x=4'
  7. The 'y=6' at the location where the dashed vertical line intersects the line of the equation we graphed

Notes

    1. The equation 'y=2x-2' is in slope-intercept form
    2. Slope-intercept form is:
    3. y=mx+b
    1. A coordinate plane consists of an x and y axis
    2. We can graph our equation '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. Our equation is 'y=2x-2', so the y-intercept, 'b', is '-2'
    4. The y-intercept is where the line of our equation passes through the y-axis
    1. Slope-intercept form is:
    2. y=mx+b
    3. Our equation is 'y=2x-2', so the y-intercept, 'b', is '-2', and the slope, 'm', is '2'
    4. The y-intercept is where the line of our equation passes through the y-axis
    5. The slope is the change in y over the change in x
    1. Our original point is (0,-2)
    2. Since the slope of the line is '2', or '2 over 1', we can move up 2 and right 1 to find our next point on the line
    3. We can keep doing this from each point we plot
    1. The dots represent the points: (0,-2), (1,0), (2,2), (3,4)
    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. Think of 'y(4)' as:
    2. "What is the value of 'y' when 'x' is 4?"
    1. Think of 'y(4)' as:
    2. "What is the value of 'y' when 'x' is 4?"
    1. Think of 'y(4)' as:
    2. "What is the value of 'y' when 'x' is 4?"
    3. The vertical line should be dashed, it's not part of our graphed equation
    4. We can find the value of 'y' when 'x' is '4' by finding where our graphed equation intersects our dashed vertical line
    1. Think of 'y(4)' as:
    2. "What is the value of 'y' when 'x' is 4?"
    3. The vertical line should be dashed, it's not part of our graphed equation
    4. We can find the value of 'y' when 'x' is '4' by finding where our graphed equation intersects our dashed vertical line
    1. Think of 'y(4)' as:
    2. "What is the value of 'y' when 'x' is 4?"
    3. The vertical line should be dashed, it's not part of our graphed equation
    4. We can find the value of 'y' when 'x' is '4' by finding where our graphed equation intersects our dashed vertical line
    1. We found the value of 'y' when 'x' is '4' by finding where our graphed equation intersected our dashed vertical line