Solution:
To find which inequality matches the graph, we will first look at the graph.
As, by looking at the graph, i observe that, the line passes through (5,1) and (-5,-4).
Equation of line passing through two points [tex](x_{1},y_{1}) {\text{and}} (x_{2},y_{2}) is =\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}[/tex].
So, equation of line passing through (5,1) and (-5,-4) is ,
[tex]\frac{y-1}{x-5}=\frac{1+4}{5+5}\\\\ 2 y -2=x-5\\\\ x -2 y+2-5=0\\\\ x - 2 y-3=0[/tex]
Putting , x=0 and y=0 in above equation of line, I get negative value, which shows point is contained inside the region of the inequality,
→x-2 y≤ 3, as this inequality is not among given options, so by taking intercept form of line,
[tex]\frac{x}{3.2}+\frac{y}{-2.3}\leq 1{\text{As slope intercept form of line is}}, \frac{x}{a}+\frac{y}{b}=1\\\\ 2.3 x-3.2 y\leq 2.3 \times 3.2 \\\\ 2.3 x-3.2 y\leq 7.36[/tex]
Which can be written as, 2 x -3 y< 7
Option (B) →2 x − 3 y < 7, is the appropriate inequality among four options which matches the graph .
