Answer:
y [tex]\leq[/tex] [tex]\frac{-1}{3}x[/tex] + 1
Step-by-step explanation:
To find the inequality represented by the graph, we need to find the linear equation that represents the blue line.
As we can see, the:
y intercept: (0, 1)
x intercept: (3, 0)
So the slope of the equation is:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
= [tex]\frac{0-1}{3-0}[/tex] = [tex]\frac{-1}{3}[/tex]
So use the slope and the slope-point formula, we find the linear expression
The standard form is: y = mx+ b
<=> y = [tex]\frac{-1}{3}[/tex] x + b
Substitute the point (0, 1) to find b, we have:
b= y - [tex]\frac{-1}{3}[/tex] x
<=> b= 1 - 0 =1
So the linear equation is: y = [tex]\frac{-1}{3}[/tex] x + 1
After that, we need to take a test point form the shaded area and evaluate the expression. Let the point be: (1, 2), we have:
2 = [tex]\frac{-1}{3} *1[/tex] +1
<=> 2=[tex]\frac{2}{3}[/tex]
We know that 2 > [tex]\frac{-1}{3}[/tex] this means that the left inequality sign is ≥ , so the inequality represented by the graph:
y [tex]\leq[/tex] [tex]\frac{-1}{3}x[/tex] + 1
