Question

Plzzz help me in this WHat inequality is represented here ???

Answer 1

Hey there!
First, you should find the equation of the line.

Recall that the equation for any line is in the form y = mx + b, where m is slope and b is y-intercept.
Remember that slope is change in y over change in x, or rise over run. Starting from (0, 4), to get to next point on the graph, let's say (1,3), the graph "rises" -1 and "runs" 1 to the right. Slope is rise/run, so slope = -1/1 = -1.
*The points you choose don't matter.

The mathematical formula for slope is
$m = \frac{(y2-y1)}{(x2-x1)}$, where one point is (x1, y1) and another point is (x2, y2).
We can still find the same answer using this formula. Choose two points, let's say (0, 4) and (4, 0)
$m = \frac{0-4}{4-0} = -1$

The y-intercept, where the graph passes through the y-axis, in this case is 4.

The equation of the line will be
y = mx + b
y = (-1)x + 4
y = -x + 4

Since this is in inequality, we need to use inequality signs.
Note that the line is a solid line, not dotted.
< If line is dotted and the area below the graph is shaded
> If line is dotted and the area above the graph is shaded
≤ If line is solid and the area below the graph is shaded
≥ If line is solid and the area above the graph is shaded

We will use ≤ for this problem because the line is solid and the area below the graph is shaded.
The inequality is
y ≤ -x + 4

Please comment if you have any questions!