Which linear inequality is represented by the graph? y ≤ 2x + 4 y ≤ x + 3 y ≥ x + 3 y ≥ 2x + 3

First we are going to find the equation of the solid line passing trough the points (0, 3) and (2, 4).

Using the slope formula:

Now we can use the point slope formula to complete the line equation:

Since the shaded region is bellow the line , the inequality represented in the graph is .

The lines represent the inequalities

Further explanation:

The linear equation with slope m and intercept c is given as follows.

The formula for slope of line with points and can be expressed as,

Given:

The inequalities are as follows.

a.

b.

c.

d.

Explanation:

The blue line intersects y-axis at therefore the y-intercept is 3.

The blue line intersect the points that are and

The slope of the line can be obtained as follows.

The slope of the line is

Now check whether the inequality included origin or not.

Substitute in equationy

0 is less than 3 which means that the inequality does include origin.

Therefore, the blue line is

Learn more:

1. Learn more about inverse of the functionhttps://.

2. Learn more about equation of circle .

3. Learn more about range and domain of the function

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear inequalities

Keywords: numbers, slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32