Answer: a. [tex]2x+y<7[/tex]
Step-by-step explanation:
We know that the intercept equation of a line is given by :-
[tex]y=mx+c[/tex], where m is the slope of the line and c is the y intercept.
From the given graph , we can see that the two points on the dotted line are(0,7) and (2,3).
The y- intercept = Value of y at x=0 =7
The slope of the line passing through two points is given by :-
[tex]m=\dfrac{\text{Change in y}}{\text{Change in x}}[/tex]
i.e. [tex]m=\dfrac{3-7}{2-0}=\dfrac{-4}{2}=-2[/tex]
Thus , the slope of the line passing through (0,7) and (2,3) :- [tex]m=-2[/tex]
Put m=-2 in the general intercept equation of line ,
[tex]y=-2x+7\\\\\Rightarrow\ 2x+y=7[/tex]
Since the line is dotted , this means that one quantity is strictly greater than other.
The graph is shaded in the left side , it means the value of the expression [tex]2x+y[/tex] is less than 7.
Hence, the inequality for the given graph will be:-
[tex]2x+y<7[/tex]
