Question

Find the inequality for this graph

Answer 1

y ≥ -2x-5

Explanation:

We have given the graph.

We have to find the inequality for this graph.

First, we find the boundary line that passes through the point (-1,-3) and (0,-5).

The slope of this equation is m = -5-(-3)/0-(-1)

m = -5+3/0+1= -2

The standard point slope form of equation :

y = mx+c

Where c is the y-intercept.

In the graph, the y-intercept is -5 so,

y = -2x-5

The inequality of the graph is :

y ≥ -2x-5

The inequality holds because one line is solid and the upper half plane is shaded.

Answer 2

`y \geqslant - 2x - 5`

EXPLANATION

First we need to find the equation of the boundary line which passes through (-1,-3) with a y-intercept of -5.

The slope of this line is

`m = ( -5 - - 3)/(0 - - 1) = - 2`

The equation of this line is

`y = - 2x - 5`

Since the boundary line is solid and the upper half plane is shaded the required inequality is

`y \geqslant - 2x - 5`