Slope Of An Equation


Rule
We can find the equation of any line by finding the slope and y-intercept. Then the equation of the line can be written in slope-intercept form, y = mx+b.
Rule

  • If we substitute 0 in for x in the equation y = mx+b, we get y = m(0)+b or y = b. Thus the graph will cross the y-axis at the point (0,b)
  • For the equation y = x+2, m = 1 and b = 2. The graph crosses the y-axis at (0,2) and has a slope equal to 1.
    		• Graph y = x+2


    Example1
    1) Find the slope and y=intercept.
    a) y = 2x + 3

    y = mx + b
    m = 2
    b = 3

    The slope is 2.
    The y-intercept is 3.


    		 b) 3x + 2y = 4

    2y = -3x + 4
    y = (-3/2) + 2
    y = mx + b
    m = -3/2
    b = 2

    The slope is -3/2.
    The y-intercept is 2.
    Try finding some slopes. Go to the Slope applet below. Follow the directions in the applet:







    Example2
    a)Graph y = (-5/2)x+5 using y-intercept and slope

  • m = -5/2
  • b = 5
  • First plot (0,5) the y-intercept
  • Now we will use the slope -5/2
  • The numerator is your vertical move: negative down, postitve up.
  • The denominator is your horizontal move: negative left, postitve right.
  • To find the next point, from the y-intercept move 5 units down (-5) and 2 units right (positive 2).
  • Repeat this procedure from this new point to get another point etc.
    		• Graph

    Try graphing some equations. Go to the Graph applet below. To graph your an equation:

  • Click on New Graph.
  • Plot the y-intercept.
  • Use the slope to plot another point.
  • Repeat the last step.
  • Now hit Draw the line




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