Question

Which linear inequality is represented by the graph?

Answer 1

The linear inequality would be y ≥ 1/2x - 1

Step-by-step explanation:

In order to find the inequality, first find the equation of the line. To do this, we start by identifying two points on the line. For the purpose of this, we'll use (0, -1) and (2, 0). Now we can use the slope formula to find the slope.

m(slope) = (y2 - y1)/(x2 - x1)

m = (0 - -1)/(2 - 0)

m = 1/2

Now that you have the slope, you can use either point and point-slope formula.

y - y1 = m(x - x1)

y - 0 = 1/2(x - 2)

y = 1/2x - 1

Now that we have this, we look to the shading. If the shading is above, then we make y ≥. If it is under the line, then we make y ≤. In this case, the shading is above. Leaving us with:

y ≥ 1/2x - 1

Answer 2

`y\geq(1)/(3)x-1`

Explanation:

Given: The graph of inequality.

First choose two points on graph and find the equation of line.

From graph two passing points are (3,0) and (0,-1)

using two point formula of line to find the equation.

`y-(-1)=(0+1)/(3-0)(x-0)`

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

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

Now we find inequality.

Line is solid on graph. Equality would be there.

point (0,0) is part of shaded region.

(0,0) must be true for above equation.

Check the points

`0 \text{___} (1)/(3)(0)-1`

`0 \text{___} -1`

As we know 0 is greater than -1.

Hence, The equation of inequality
`y\geq(1)/(3)x-1`