Question

Find the inequality represented by the graph

Answer 1

`y\leq -(1)/(3)x+1`

Explanation:

Given:

From the graph, the x and y intercepts are at the points (3, 0) and (0, 1) respectively.

Now, for a line with two points
`(x_1,y_1)\ and\ (x_2,y_2)`, the slope is given as:

`m=(y_2-y_1)/(x_2-x_1)`

Here,
`(x_1,y_1)=(3,0)\ and\ (x_2,y_2)=(0,1)`. Therefore,

`m=(1-0)/(0-3)=-(1)/(3)`

Now, y-intercept is
`b=1`

Therefore, the standard form of a line is of the form:
`y=mx+b`. So, the equation of the line on the graph is:

`y=-(1)/(3)x+1`

Now, from the graph, the region is below the line including all the points on the line. Therefore, the inequality used is less than or equal to. This gives,

`y\leq -(1)/(3)x+1`