Graphs Using Slope-Intercept Form

Key Questions

  • How do you know if you graphed the linear equation correctly?

    If your line goes through two distinct points of the equation, then your line is correct.

    I hope that this was helpful.

    Wataru · 1 · Nov 9 2014
  • Once you graph the y-intercept, how do you determine the second point?

    You can choose any nonzero value #x_2# for #x# and plug it into the equation of the line you are working on to find the corresponding #y#-coordinate #y_2#. Your second point is #(x_2,y_2)#.

    I hope that this was helpful.

    Wataru · 1 · Nov 1 2014
  • How do you graph a line using slope-intercept form?

    The equation of a line in explicit form is:

    #y=mx+q#, where #m# is the slope and #q# the y-intercept.

    It is easier to show the procedure with some example:

    #y=2#: this line is parallel to the x-axis and it passes from the point #P(0,2)#.

    #x=3#: this line is parallel to the y-axis and it passes from the point #P(2,0)#.

    #y=x+1#: this line is parallel to the bisector of the I and III quadrants and it passes from the point #P(0,1)#.

    graph{x+1 [-10, 10, -5, 5]}

    #y=-x-1#: this line is parallel to the bisector of the II and IV quadrants and it passes from the point #P(0,-1)#.

    graph{-x-1 [-10, 10, -5, 5]}

    #y=2/3x+1#: we have to find the point #P(0,1)#, from this point we have to "count" 3 units to the right and then 2 units to the up, so we can find the point #Q(3,3), then we have to join the two point found.

    graph{2/3x+1 [-10, 10, -5, 5]}

    #y=-1/2x-1#: we have to find the point #P(0,-1)#, from this point we have to "count" 2 units to the left and then 2 units to the up, so we can find the point #Q(-2,0), then we have to join the two point found.

    graph{-1/2x-1 [-10, 10, -5, 5]}

    The difference in these two last examples is the "choice" of the "right" and the "left". Right, if the #m# is positive; left, if the #m# is negative.

    Massimiliano · 1 · Jan 30 2015

Questions

Graphs of Linear Equations and Functions