Question

Solve the inequalities by graphing. Select the correct graph. y > 2x y < 3

Answer 1

Answer:

The graph is shown below.

Step-by-step explanation:

Given:

The inequalities to solve by graphing are given as:

$y>2x\\\\y$

Now, in order to graph them, we first replace inequality sign by equal to sign.

So, the two equations are given as:

$y=2x\\\\y=3$

Now, the first equation is a straight line of the form $y=mx$. This is a line that passes through origin with slope equal to 'm'.

So, the slope of the first line is 2.

In order to plot the line,we take a random value of 'x'. Let $x=1$

So, $y=2\times 1=2$

So, the point on the line is (1, 2)

Now, we draw a line passing through the points (0, 0) and (1, 2). This is the line for the first equation.

Now, the second equation is a straight line parallel to the x-axis.

So, the equation $y=3$ is a straight line parallel to x-axis passing through the point (0, 3) as shown below.

Now, since the first inequality has 'y' greater than '2x'. So, the solution region is left of the line excluding the line.

Also, the second inequality has 'y' less than 3. So, the solution region is below the line excluding the line.

The common region for both the line inequalities is the solution.

The solution region is shown below.