Question

Which inequality is represented by the graph?

Which point is a solution to the inequality?

Answer 1

The first answer is : y > 2x + (3/4)

The second answer is : (2, 5)

Answer 2

`y > 2x + 0.75`

Explanation:

We are given the following information:

The line in the graph passes through two points (0,0.75), (2,4.75)

We will find the equation of this straight line with the help of two point equation of straight line.

The equation of line is given by:

`(y-y_1) = \displaystyle(y_2-y_2)/(x_2-x_1)(x-x_1)`

where,
`(x_1,y_1), (x_2.y_2)` is the point through which the line passes.

The equation of line is:

`(y-0.75) = \displaystyle(4.75 - 0.75)/(2-0)(x-0)\\\\(y-0.75)= 2x\\y = 2x + 0.75`

This line is not a part of the shaded region. Also shaded region lies on the left side of the line.

Hence, the inequality represented by graph is:

`y > 2x + 0.75`

Out of the given points, (2,5) satisfies the above inequality.

`y > 2x + 0.75\\5 > 4 + 0.75 = 4.75`