Question

NEED HELP ASAP

Select the correct answer.
4
X
-4
2
-2
Which of the following inequalities is graphed on the coordinate plane?
O A. y > -21 + 1
OB. y -23 + 1
OC. y < -25 + 1
OD. y < -23 + 1

Answer 1

Answer: D. y ≤ -2x = 1

Explanation: To determine the inequality, first determine the line equation.

Line equation can be written as

`y-y_(0)=m(x-x_(0))` , called point-slope form of a line equation,

where

m is slope of the equation

x₀ and y₀ are points in the line

Slope is calculated as the difference between y-coordinates divided by the difference between the x-coordinates:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

From the graph, we have 2 points: (-1,3) and (1,-1), so find slope:

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

m = -2

Replacing slope and point (0,1) into point-slope form:

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

`y=-2x+1`

This is the equation of the line.

Now, we determine the inequality:

Observe the graph, if the line is a continuous one, it is a less-than-or-equal-to (≤) or more-than-or-equal-to (≥). If it was a dotted line, the symbol would be less-than (<) or more-than (>).

In our case, the line is continuous so it will be ≥ or ≤. To determine which one, we can plug a point located in the shaded part, for example (0,0). Substituting:

y = -2x + 1

0 ≠ -2(0) + 1

0 ≤ 1

Therefore, line equation of the graph is
`y\leq -2x+1`.