Question

State the inequality that represents the graph below. Show steps used to find the inequality. HELPPPPP

Answer 1

The inequality representing the graph shown in figure is -

y < 6x + 3.

[Refer to the graph plotted at the end for confirmation]

What is Inequality?

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. The L.H.S and R.H.S of an inequality are not equal.

Given is a graph of an inequality plotted on graph paper.

The following steps are to be followed in order to find the inequality -

STEP 1 - Determining inequality type.

From the graph, it can be seen that the the border line dividing the green shaded area from the remaining graph is uniform i.e. not dashed. Therefore, the inequality is a strict inequality which means that, either inequality sign is '>' or '<'. The sign cannot be ≤ or ≥.

STEP 2 - Determining the inequality equation.

From the graph, it can be seen that the y - intercept of line is (0, 3). The line cuts the x - axis at coordinates (- 0.5, 0). Therefore, it can be concluded that -

y - intercept = 3

x - intercept = - 0.5

Then, the slope of line will be = [m] = | 3 - 0/0 -(- 0.5) | = |3/0.5| = 6

The general equation of line with slope 'm' and y - intercept is -

y = mx + c

y = 6x + 3

Therefore, y = 6x + 3 is the equation of straight line.

STEP 3 - Determining the side to be shaded.

For this, take the origin (0, 0) and test it with both the inequalities '>' and '<'.

For inequality → greater than ' > ' -

y > 6x + 3

Put (x, y) as (0, 0), we get -

0 > 6 x 0 + 3

0 > 3

Which is false.

For inequality → less than ' < ' -

y < 6x + 3

Put (x, y) as (0, 0), we get -

0 < 6 x 0 + 3

0 < 3

which is true.

So our final inequality is → y < 6x + 3.

Therefore, the inequality representing the graph shown in figure is -

y < 6x + 3.

[The graph for this inequality is attached below]

To solve more questions on graphical inequalities, visit the link below-

brainly.com/question/23724758

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