Write The Following Inequality In Slope-intercept Form. 20 X − Y \textless 18 20x - Y \ \textless \ 18 20 X − Y \textless 18 Write Your Answer With Y First, Followed By An Inequality Symbol. Use Integers, Proper Fractions, And Improper Fractions In Simplest Form. □ \square □

Introduction

In mathematics, inequalities are a fundamental concept that helps us compare values and make decisions. One of the most common forms of inequalities is the slope-intercept form, which is used to represent linear equations and inequalities. In this article, we will focus on solving the inequality $20x - y \ \textless \ 18$ in slope-intercept form.

Understanding Slope-Intercept Form

The slope-intercept form of a linear equation is given by the equation $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. This form is called the slope-intercept form because the slope is the coefficient of the $x$ term, and the y-intercept is the constant term.

Solving the Inequality

To solve the inequality $20x - y \ \textless \ 18$, we need to isolate the variable $y$ on one side of the inequality. We can do this by adding $y$ to both sides of the inequality, which gives us:

$$20x - y + y \ \textless \ 18 + y$$

Simplifying the left-hand side of the inequality, we get:

$$20x \ \textless \ 18 + y$$

Now, we need to isolate the variable $y$ on the right-hand side of the inequality. We can do this by subtracting $18$ from both sides of the inequality, which gives us:

$$20x - 18 \ \textless \ y$$

Finally, we can rewrite the inequality in slope-intercept form by dividing both sides of the inequality by $-1$, which gives us:

$$y \ \textgreater \ -20x + 18$$

Interpreting the Solution

The solution to the inequality $20x - y \ \textless \ 18$ is $y \ \textgreater \ -20x + 18$. This means that for any value of $x$, the corresponding value of $y$ must be greater than $-20x + 18$. In other words, the graph of the inequality is a line with a slope of $-20$ and a y-intercept of $18$.

Graphing the Inequality

To graph the inequality, we can use a graphing calculator or a computer program. We can also use a coordinate plane to plot the line and shade the region that satisfies the inequality.

Conclusion

In this article, we solved the inequality $20x - y \ \textless \ 18$ in slope-intercept form. We isolated the variable $y$ on one side of the inequality and rewrote the inequality in slope-intercept form. We also interpreted the solution and graphed the inequality using a coordinate plane.

Tips and Tricks

• When solving inequalities, it's essential to isolate the variable on one side of the inequality.
• When rewriting an inequality in slope-intercept form, make sure to divide both sides of the inequality by the correct coefficient.
• When graphing an inequality, use a coordinate plane to plot the line and shade the region that satisfies the inequality.

Common Mistakes

• When solving inequalities, it's easy to make mistakes by adding or subtracting the wrong terms.
• When rewriting an inequality in slope-intercept form, make sure to divide both sides of the inequality by the correct coefficient.
• When graphing an inequality, it's easy to forget to shade the region that satisfies the inequality.

Real-World Applications

Inequalities are used in many real-world applications, such as:

• Finance: Inequalities are used to compare interest rates and investment returns.
• Science: Inequalities are used to compare physical quantities, such as temperature and pressure.
• Engineering: Inequalities are used to compare design parameters, such as stress and strain.

Conclusion

Introduction

In our previous article, we solved the inequality $20x - y \ \textless \ 18$ in slope-intercept form. We isolated the variable $y$ on one side of the inequality and rewrote the inequality in slope-intercept form. In this article, we will answer some common questions about solving inequalities in slope-intercept form.

Q: What is the slope-intercept form of a linear equation?

A: The slope-intercept form of a linear equation is given by the equation $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Q: How do I isolate the variable on one side of the inequality?

A: To isolate the variable on one side of the inequality, you need to add or subtract the same term from both sides of the inequality. For example, if you have the inequality $20x - y \ \textless \ 18$, you can add $y$ to both sides of the inequality to get $20x \ \textless \ 18 + y$.

Q: How do I rewrite the inequality in slope-intercept form?

A: To rewrite the inequality in slope-intercept form, you need to divide both sides of the inequality by the correct coefficient. For example, if you have the inequality $20x \ \textless \ 18 + y$, you can divide both sides of the inequality by $-1$ to get $y \ \textgreater \ -20x + 18$.

Q: What is the y-intercept of the inequality?

A: The y-intercept of the inequality is the value of $y$ when $x$ is equal to zero. In the inequality $y \ \textgreater \ -20x + 18$, the y-intercept is $18$.

Q: How do I graph the inequality?

A: To graph the inequality, you can use a graphing calculator or a computer program. You can also use a coordinate plane to plot the line and shade the region that satisfies the inequality.

Q: What are some common mistakes to avoid when solving inequalities?

A: Some common mistakes to avoid when solving inequalities include:

• Adding or subtracting the wrong terms
• Dividing both sides of the inequality by the wrong coefficient
• Forgetting to shade the region that satisfies the inequality

Q: What are some real-world applications of inequalities?

A: Inequalities are used in many real-world applications, such as:

• Finance: Inequalities are used to compare interest rates and investment returns.
• Science: Inequalities are used to compare physical quantities, such as temperature and pressure.
• Engineering: Inequalities are used to compare design parameters, such as stress and strain.

Q: How do I check my work when solving inequalities?

A: To check your work when solving inequalities, you can:

• Plug in a test value for $x$ and check if the corresponding value of $y$ satisfies the inequality.
• Graph the inequality and check if the region that satisfies the inequality is correct.
• Use a calculator or computer program to check your work.

Conclusion

In conclusion, solving inequalities in slope-intercept form is a fundamental concept in mathematics. By isolating the variable on one side of the inequality and rewriting the inequality in slope-intercept form, we can solve inequalities and interpret the solution. We can also graph the inequality using a coordinate plane and use it to make decisions in real-world applications.