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Chapter 4: Problem 551

Graph the linear inequality \(x \geq 0\)

Short Answer

Expert verified
Graph a vertical solid line at \(x = 0\) and shade the region to the right.

Step by step solution

01

Understand the Inequality

The inequality given is \(x \geq 0\). This means that we need to graph the region of the coordinate plane where the x-values are greater than or equal to zero.
02

Graph the Boundary Line

Plot the line \(x = 0\) on the coordinate plane. This line is a vertical line that intersects the x-axis at zero. Since the inequality is \(x \geq 0\) and contains an equality, the line itself will be included in the solution, so draw it as a solid line.
03

Determine the Shading

Since the inequality is \(x \geq 0\), the solution includes all points to the right of and including the line \(x = 0\). Shade the region to the right of the line to represent all x-values greater than or equal to zero.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

linear inequalities
Linear inequalities are similar to linear equations but with inequalities instead of an equal sign (e.g., \(\text{x} \geq 0\)). They represent a range of values rather than a single value. When you solve a linear inequality, you're finding the set of all possible solutions that make the inequality true.
coordinate plane
The coordinate plane is a two-dimensional plane formed by the intersection of a vertical line (y-axis) and a horizontal line (x-axis). These lines divide the plane into four quadrants. It is used to graph equations and inequalities. Each point on the plane is represented by an ordered pair \((x, y)\), where \(\text{x}\) is the horizontal distance from the origin and \(\text{y}\) is the vertical distance.
graphing boundary lines
To graph a linear inequality, you first need to graph the boundary line. For the inequality \(\text{x} \geq 0\), the boundary line is \(\text{x} = 0\). This is always a vertical line crossing the x-axis at zero. Since our inequality includes the equal sign (\(i.e., \text{x} \geq 0\))), the boundary line is solid, indicating that points on the line are included in the solution.
shading regions
The final step is to determine which side of the boundary line to shade. For the inequality \(\text{x} \geq 0\), you shade the region to the right of the boundary line because this represents all the points where \(\text{x}\) is greater than or equal to zero. If the inequality were \(\text{x} > 0\), you would still shade to the right, but the boundary line would be dashed to show that points on the line are not included.

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Most popular questions from this chapter

Money. Gerry wants to have a maximum of $$\$ 100$$ cash at the ticket booth when his church carnival opens. He will have $$\$ 1$$ bills and $$\$ 5$$ bills. If \(x\) is the number of $$\$ 1$$ bills and y is the number of $$\$ 5$$ bills, the inequality $$x+5 y \leq 100$$ models the situation. (a) Graph the inequality. (b) List three solutions to the inequality \(x+5 y \leq 100\) where both x and y are integers.

Find the equation of a line containing the given points. Write the equation in slope-intercept form. (-3,0) and (-7,-2)

Graph the linear inequality \(y>4 x\)

Graph the linear inequality \(y<-3 x-4\)

Find the equation of each line. Write the equation in slope-intercept form. Perpendicular to the line \(y-1=0\), point (-2,6)
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