Please Help Choose the system of inequalities that matches the graph below. coordinate plane with a solid line through points (0, 7) and (1, 6). A dashed line passes through points (0, 11) and (–1, 8). There is yellow shading below the solid line and blue shading above the dashed line. The shading turns green in the overlap. x + y –11

Question

Please Help Choose the system of inequalities that matches the graph below. coordinate plane with a solid line through points (0, 7) and (1, 6). A dashed line passes through points (0, 11) and (–1, 8). There is yellow shading below the solid line and blue shading above the dashed line. The shading turns green in the overlap. x + y < 7 3x – y less than or equal to –11 x + y less than or equal to 7 3x – y < –11 x + y > 7 3x – y greater than or equal to –11 x + y greater than or equal to 7 3x – y > –11

danmac0710 · Answer

Any chance you could paste the graph in please or is understanding the verbal decsription part of the problem? You should at least draw a graph to get started, and then take test points in each region to establish which inequality(ies) the point satisfies. Doing this will help you label the lines with the correct inequality. I hope this helps.

anonymous · Answer

Sorry, here it is

danmac0710 · Answer

I don't think that is the correct graph for the question ytou asked. You have to find an equation linking x and y from the inequations (aka inequalities) you were given. x+y <7 leads to y = -x + 7. So when y=0 on this line, x=7, so one of the lines on the graph given should have had a x-axis-intercept (you know, where y=0) of 7. I cannot see the point (7,0) on either line. Am I missing something?

anonymous · Answer

Ah, omigosh sorry again you're right. I'm new here, I'm positive this is the right one. Thanks for helping me out, by the way.

anonymous · Answer

Have you determined equations for the two lines?  The solid line passes through (0, 7) and (1, 6).  What would the equation of this solid line look like?

Remember the equation for slope:

$$m = \frac{ y _{2} - y _{1} }{ x _{2} - x _{1} }$$

And the equation for a line:

$$y - y _{1} = m(x - x _{1})$$

After you determine the equation of this solid line, we could then determine which inequality is associated with it.  We notice the region underneath this line is shaded yellow, so that clues us in that it will be a less than inequality.  The fact that the line is solid tells us that it is also equal.  So the inequality associated with the solid line is "less than or equal".  All we need is the equation for the line.