Question

Find the equality represented by the graph?

Answer 1

`-x+4y<12`

Explanation:

Given: graph

To find:the inequality

Solution:

Equation of a line passing through points
`(x_1,y_1),(x_2,y_2)` is given by
`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Take
`(x_1,y_1)=(0,3),(x_2,y_2)=(4,4)`

So,equation of line is evaluated as follows:

`y-3=(4-3)/(4-0)(x-0)\\ y-3=(x)/(4)\\ 4y-12=x\\-x+4y=12`

As per the graph,inequality is
`-x+4y<12`

Here, use sign < and not
`\leq` as line in the graph is dotted that is points on the line are excluded.