y<2x-1 graphing line

Question

 

graph on a coordinate plane

 

y<2x-1

Answer 1

Hi Nunii,  First let's look at the similar-looking equation y=2x-1.  This is in the y=mx+b form, and we know we have a straight line with a slope (m) = +2, and when x=0, the line crosses the y axis at -1, just below the x-axis.  By trying a few other values for x, we can calculate y and plot other points for our line graph:

x=+1, y=+1;  x=+2, y=+3;  x=-1, y=-3;  x=-2, y=-5.   So we have a straight line from upper right down to lower left, crossing the vertical y-axis at x=-1.

Now let's change the equal (=) sign to a less than (<) sign:  y < 2x-1

That means y can be any value (amount) that is less than what we calculate when y = 2x-1  So now our 

y = 2x-1 line becomes our upper boundary, just above the highest (most positive) values that y can be...  

[Later in learning math, we call that line our limit for y, which is a function of x (changes value depending on what values x is).  y=f(x) simply means y varies as a function of x].  

Now, rather than just a line, our graph becomes the entire area on the graph (and beyond, out to infinity), of all values below our y = 2x-1 line, but never quite touches that line.  We normally show that on a graph by shading-in that entire area on the graph, which is the lower-right side of our diagonal graph line of y = 2x-1.  Make sense?  Google "Graph y<2x-1" to see online similar examples.