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What's Slope-Intercept Form of a Linear Equation?

Definition: Slope-Intercept Form

Summary

  1. Slope-intercept form is one way of writing a linear equation
  2. Slope is represented by 'm'
  3. The y-intercept is where the line crosses the y-axis
  4. The x-coordinate is always 0 and the y-coordinate is represented by 'b'

Notes

    1. Slope-intercept form is one way of writing a linear equation
    2. It is useful when you know the slope and the y-intercept of a line
    1. The slope tells you how steep the line is
    2. It's just the change in y over the change in x, or the RISE over RUN
    1. The y-axis is the VERTICAL axis
    2. The point where the line intersects the y-axis is called the y-intercept
    1. The y-intercept is the point where x=0
    1. Remember, the origin is the point (0,0)
    2. Since we know that the x-coordinate of our line is 0, we just move up or down the y-axis 'b' units
    1. The y-axis is the line where x=0
    2. So any point on the y-axis has an x value of 0
    1. Remember, b, the y-coordinate, tells us how many units we move up or down
    1. If we know the slope and y-intercept, slope-intercept form makes it really easy to write the equation
    1. If we know the slope and y-intercept, slope-intercept form makes it really easy to write the equation
    2. 'm' is the slope of the line
    3. 'b' is the y-intercept, or where the line crosses the vertical axis
    1. If you know this information, you can then draw the graph of the equation
    1. So we know that our value for m, the slope, will be 2
    2. Remember, 'm' represents the slope of the line
    1. Slope is just the steepness of the line
    1. 3, the y-coordinate of the intercept, is our value for 'b'
    1. We can just plug our values for 'm' and 'b' into the formula
    1. 2 is the slope, represented by 'm'
    1. 3 is the y-intercept, represented by 'b'
    1. This is the equation of our line in slope-intercept form
    1. Slope-intercept form is one way of writing an equation
    2. Linear equations can also be written in standard form or point-slope form
    3. You can use any form to write an equation, but slope-intercept is easiest if you know the slope and the y-intercept