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Step-by-Step Explanation:

We want to find the slope-intercept inequality for the graph shown.

First, we will need to determine the equation of the line. We are given two points: (1, -1) and (2, -5). Let’s use the two to determine the slope. The slope formula is given by:

Let (1, -1) be (x₁, y₁) and let (2, -5) be (x₂, y₂). Substitute appropriately:

So, our slope is -4.

Now, we can use the point-slope form:

Where m is the slope and (x₁, y₁) is a point.

So, let’s substitute -4 for m. For consistency, we will let (1, -1) be (x₁, y₁). Hence:

Distribute:

Subtract 1 from both sides:

Finally, we can determine our sign.

Notice that our line is dotted. Therefore, we do not have “or equal to.”

Also, notice that the area shaded is below our line. Therefore, our y is less than our equation .

So, our symbol should be ”less than.”

Therefore, our equation is:

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We need to find the equation for the boundary line. It goes through the two points (1,-1) and (2,-5)

Find the slope of the line through (x1,y1) = (1,-1) and (x2,y2) = (2,-5)

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

m = (-5 - (-1))/(2 - 1)

m = (-5 + 1)/(2 - 1)

m = -4/1

m = -4  is the slope

Plug m = -4 and (x1,y1) = (1,-1) into the point slope formula. Solve for y.

y - y1 = m(x - x1)

y - (-1) = -4(x - 1)

y + 1 = -4(x - 1)

y + 1 = -4x + 4   ... distributing

y + 1 - 1 = -4x + 4 - 1  ... subtracting 1 from both sides

y = -4x + 3  is the equation of the boundary line

The blue shaded region tells us to consider all points below this boundary line as solutions. So we will use a "less than" sign to indicate this

We go from y = -4x+3 to y < -4x+3  which is the answer we want.

We do not have a line under the inequality sign. Simply because the boundary is a dashed line, so we exclude points on the boundary line as solutions. If we had , then the boundary line would be solid and it would tell the reader "points on the boundary line are part of the solution set".

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.

idk

step-by-step explanation: