vef said:
iv'e been given a graph with a shaded region and been asked what the contrants of the regoin are ( i have a choice of 8) prob is i have no idea how to even start - i'm a distance learning student & cant get hold of my tutor & i need to submit my assigment
what i'd like to know is how do i draw one of these graphs to work out the answer
for example one of the options is y >4x-5 - how do i draw this on a graph to see if it fits the example ive been given
thanx
The region y > 4x - 5 is formed by the
line y = 4x - 5.
Start by graphing the line. y = 4x - 5 is in slope-intercept form. The y-intercept is -5, so you can start by plotting a point at -5 on the y-axis. The slope is 4, or 4/1. As you move to the right along the line, a rise of 4 units is accompanied by a run of 1 unit (recall that slope is rise/run).
Start at the point (0, -5) which you plotted on the y-axis. Move UP 4 units and TO THE RIGHT 1 unit, and you'll be at (1, -1). Plot another point here. You can do this again....go UP 4 units and TO THE RIGHT 1 unit and you'll be at (2, 3). This is another point on the line. Now, take a ruler and draw a dashed line that goes through the points you've plotted (it is a dashed line rather than a solid line because the points ON the line don't satisfy the inequality).
Finally, you need to shade the points on one side of the line. Pick a point on one side of the line and test its coordinates in the original inequality. If your test point makes the inequality true, shade the region containing the test point. If the test point does not make the inequality true, shade the region on the OTHER side of the line. For example, the origin (0, 0) does not lie on the line y = 4x - 5, so let's use it as a test point. Substitute into the original inequality y > 4x - 5:
0 > 4*0 - 5
0 > -5
This is true, so shade the region containing the origin. This is the graph of y > 4x - 5.
I hope this helps you.
