Question

Solve and graph: y>2x-1

Answer 1

To begin you must plot the graph y=2x-1.
If you can already do this disregard the next 2 paragraphs.
There are two ways you can plot this line. The first and fastest way is to use the gradient intercept method.

The basic format of a straight line is y=mx+b where m is the gradient and b is the y intercept. In this case the gradient is 2 and the y intercept is -1. Gradient is expressed as rise over run, so this graph will rise two units of y for every one of x. Knowing these two basic facts you can plot the line. Draw up your axes and plot you y intercept, which is where x=0 so it will be at (0,-1). Now since we know that the graph rises 2 for every 1 across, we plot a point 2 above that and 1 across, at the point (1,1). Now simply join the two points (with a dotted line for less than or more than or a solid line for less than or equal to or more than or equal to).

The second method is to substitute x values and solve for y, so you would substitute x=1 then solve to find at the point where x=1, y=1 therefore (1,1) is a point on your line. Now do this for any other one number draw a line going through the points (with a dotted line).

Now that we have the line you need to find which region of the graph the inequality specifies. To do this, pick a test point, any not on the line will work. For simplicities sake let's pick (0,0) now sub the x and y values into your original inequality and solve:
y>2x-1
0>2(0)-1
0>0-1
0>-1 is true, therefore the inequality describes the region above the line, which should be shaded.

So in short, the inequality is graphed as a dotted line at y=2x-1 and the region above the line is shaded.