Which number completes the system of linear inequalities represented by the graph?
y > = 2x – 2 and x + 4y > = ?

we have

------> inequality A

The inequality A is the solid red line in the graph

the solution of the inequality A is the shaded area above the solid red line

------> inequality B

The inequality B is the solid blue line in the graph

the solution of the inequality B is the shaded area above the solid blue line

we know that

the point lie on the line of the inequality B

substitute the values of x and y in the equation of the line

so

the equation of the line B is

the equation of the inequality B is

therefore

the answer is

The number is

The number is in the inequality .

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,

Explanation:

The orange line intersects y-axis at , therefore the y-intercept is -2.

The orange line intersect the points that are and .

The slope of the line can be obtained as follows.

The slope of the line is m = 2.

Therefore, the orange line is .

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 .

The inequalities is passes through the point .

The number is – 12.

The number is in the inequality .

Learn more:

1. Learn more about inverse of the function link.

2. Learn more about equation of circle link.

3. Learn more about range and domain of the function link

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.

0 is its x and y coordinate