Question

Which of the following inequalities matches the graph?

Answer 1

The correct answer to this question is

A. 2x + y < 7

Answer 2

Answer: a.
`2x+y<7`

Explanation:

We know that the intercept equation of a line is given by :-

`y=mx+c`, 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 :-

`m=\frac{\text{Change in y}}{\text{Change in x}}`

i.e.
`m=(3-7)/(2-0)=(-4)/(2)=-2`

Thus , the slope of the line passing through (0,7) and (2,3) :-
`m=-2`

Put m=-2 in the general intercept equation of line ,

`y=-2x+7\\\\\Rightarrow\ 2x+y=7`

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
`2x+y` is less than 7.

Hence, the inequality for the given graph will be:-

`2x+y<7`