Question

Which inequality is represented by this graph?5(0.1)(5,0)5-5O A. y >- x+1B. yy<- 6x +1C. 72-*x+1D. ys-x+1

Answer 1

We can see a graph representing an inequality. We also can see that we have two points (two coordinates) that lie on a line, and since we have a dotted line, we need to use an inequality symbol that does not take into account the values of the line, that is, we need to use < or >.

Now, to find the expression of the inequality on the graph, we need to proceed as follows:

1. Find the equation of the line using the given points: (0, 1) and (5, 0).

We can use the two-point form of the line to find the equation:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

And now we can label both points as follows:

• (0, 1) ---> x1 = 0, y1 = 1

,

• (5, 0) ---> x2 = 5, y2 = 0

And we can substitute these values into the above equation:

`\begin{gathered} y-y_(1)=(y_(2)-y_(1))/(x_(2)-x_(1))(x-x_(1)) \\ \\ y-1=(0-1)/(5-0)(x-0) \\ \\ y-1=(-1)/(5)x \\ \\ y-1+1=-(1)/(5)x+1 \\ \\ y=-(1)/(5)x+1 \\ \end{gathered}`

2. We need to use a test point to find the direction of the inequality. Since we can see that the point (0, 0) is part of the shaded part of the inequality, we can substitute this point in the line equation above as follows:

`\begin{gathered} x=0,y=0 \\ \\ 0=-(1)/(5)(0)+1 \\ \\ 0<1 \\ \end{gathered}`

And we can see that the inequality is of the form (<).

Therefore, in summary, the expression that represents the inequality is:

`y<-(1)/(5)x+1`

(Option B).