Question 23362
NOTE:  If you have trouble graphing a straight line, with slope and y-intercept, see my NEW lesson plans in algebra.com for this topic under the heading of "Graphing."


For the inequality {{{y >= 2x+3}}}, first graph the equation {{{y = 2x+3}}}, which is in slope-intercept form, with y-intercept at y=3, and slope = {{{ (rise)/(run)= 2/1}}}.  Begin by graphing the y-intercept by going up 3 units on the y-axis and put a point.  From this point go UP 2 units, then go 1 unit to the right, and put another point.  Connect the points, and that's your graph, which should look like this:  

{{{graph (400,400, -10,10,-10,10, 2x+3)}}}

Now because the problem is {{{y >= 2x+3}}}, with a >=, this means to shade ABOVE the line, and INCLUDE THE LINE, so draw the line SOLID.  I can't do that shading with algebra.com, so you will have to do that for yourself.
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For the inequality {{{y > -3x-1}}}, first graph the equation {{{y = -3x-1}}}, which is in slope-intercept form, with y-intercept at y=-1, and slope = {{{ (rise)/(run)= -3/1}}}.  Begin by graphing the y-intercept by going down 1 units on the y-axis and put a point.  From this point go DOWN 3 units, then go 1 unit to the right, and put another point.  Connect the points, and that's your graph, which should look like this:  

{{{graph (400,400, -10,10,-10,10, -3x-1)}}}

Now because the problem is {{{y > -3x-1}}}, with a >, this means to shade ABOVE the line, but do NOT INCLUDE THE LINE, so draw the line DOTTED.  AS in the previous problem I can't draw the dotted line and I can't shade the graph in algebra.com, so you will have to do that for yourself.


R^2 at SCC