Answer: D. y ≤ -2x = 1
Step-by-step explanation: To determine the inequality, first determine the line equation.
Line equation can be written as
[tex]y-y_{0}=m(x-x_{0})[/tex] , 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:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
From the graph, we have 2 points: (-1,3) and (1,-1), so find slope:
[tex]m=\frac{3+1}{-1-1}[/tex]
m = -2
Replacing slope and point (0,1) into point-slope form:
[tex]y-1=-2(x-0)[/tex]
[tex]y=-2x+1[/tex]
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 [tex]y\leq -2x+1[/tex].
