Question

Which inequality matches the graph?
**picture in comments

Answer 1

@satellite73 @Hero @Luigi0210

Answer 2

hint: we have a solid line so we need the inequality to have
\[\geq \] or \[\leq \]
another hint: let (0,0) be a test point. plug in x =0 and y = 0 to see if it works. By the looks of the graph, it seems that the test is gonna fail because (0,0) isn't shaded. find that false case!

Answer 3

If you realize, the straight line cross with y-axis at (aprox) (0 , 3.5) and with the x-axis at (aprox) (-2.5 , 0), and the formula of the slope is
\[m=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]
replacing we get
\[\frac{ 3.5 - 0 }{ 0 - -2.5 }=\frac{ 3.5 }{ 2.5 }=\frac{ 7 }{ 5 }\]
and with the formula of point-slope
\[y-y _{1}=m(x-x _{1})\]
replacing we get
\[y-3.5=\frac{ 7 }{ 5 } (x-0)\]
which is equal to
\[y=\frac{ 7 }{ 5 }x+\frac{ 7 }{ 2 }\]
but aparently the point isnt (-2.5 , 0) so the best aproximation is the alternative C, im sorry but i cant see the exact point :(

Answer 4

nice one @Natriumhydrid even I got it as C too... in a different way based on using (0,0) as a test point and see that the graph doesn't have (0,0) shaded it means that plugging in x = 0 and y =0 into one of the inequalities with the greater than sign will produce a false result. Moreover, we have a solid line, so we have to look for an inequality that's false and has the \[\geq \] sign.
\[-3x+2y\geq 7\]