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y < -1/4 x +1

Step-by-step explanation:

Find two points on the dotted line

( 0,1) and  (4,0)

We can use the slope formula

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

    = (0-1)/(4-0)

    = -1/4

The slope is -1/4

The y intercept is where it crosses the y axis  or 1

The equation of the line, using slope intercept form

y = mx+b

y = -1/4x +1

The line is dotted which means there is no equals, just greater than or less than.  It is shaded below which means less than

y < -1/4 x +1

Step-by-step explanation:

First, let's find the equation of the line.

From the graph, we can pick out two points to use: (0,1) (the y-intercept) and (4,0) (the x-intercept).

Find the slope. Let (0,1) be x₁ and y₁ and let (4,0) be x₂ and y₂

Find the slope:

Substitute:

Use the slope-intercept form:

Where m is the slope and b is the y-intercept.

We already know the slope is -1/4 and the y-intercept is 1. So, substitute:

Now, replace the equal sign with an inequality. Note that the line is dotted, so we won't use "or equal to." Also note that the blue, shaded area is below the line. Thus, we will use less than. Therefore:

The sentences:

First, we picked out two points from the graph. Next, we used those two points to find the slope. We used the slope and one of the points to write our slope-intercept equation. Afterwards, we can determine from the graph that since the shaded area is below the dotted line, the equation must have a less than.

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