Find The $y$-intercept Of The Line $11x - 8y = -1$. Write Your Answer As An Integer Or As A Simplified Proper Or Improper Fraction, Not As An Ordered Pair. $\square$

by ADMIN 170 views

Introduction

In mathematics, the $y$-intercept of a linear equation is the point at which the line crosses the $y$-axis. It is the value of $y$ when $x$ is equal to zero. In this article, we will learn how to find the $y$-intercept of a linear equation in the form $ax + by = c$, where $a$, $b$, and $c$ are constants.

What is the $y$-intercept?

The $y$-intercept is the point on the line where $x$ is equal to zero. This means that the $y$-intercept is the value of $y$ when the line crosses the $y$-axis. To find the $y$-intercept, we need to substitute $x = 0$ into the equation and solve for $y$.

Finding the $y$-intercept of a Linear Equation

To find the $y$-intercept of a linear equation in the form $ax + by = c$, we need to follow these steps:

  1. Substitute $x = 0$ into the equation: Replace $x$ with zero in the equation.
  2. Solve for $y$: Simplify the equation and solve for $y$.

Example: Finding the $y$-intercept of the Line $11x - 8y = -1$

Let's find the $y$-intercept of the line $11x - 8y = -1$. To do this, we need to substitute $x = 0$ into the equation and solve for $y$.

Step 1: Substitute $x = 0$ into the equation

11(0)−8y=−111(0) - 8y = -1

Step 2: Solve for $y$

−8y=−1-8y = -1

y=−1−8y = \frac{-1}{-8}

y=18y = \frac{1}{8}

Therefore, the $y$-intercept of the line $11x - 8y = -1$ is $\frac{1}{8}$.

Conclusion

In this article, we learned how to find the $y$-intercept of a linear equation in the form $ax + by = c$. We also found the $y$-intercept of the line $11x - 8y = -1$, which is $\frac{1}{8}$. The $y$-intercept is an important concept in mathematics, and it has many real-world applications.

Key Takeaways

  • The $y$-intercept is the point on the line where $x$ is equal to zero.
  • To find the $y$-intercept, we need to substitute $x = 0$ into the equation and solve for $y$.
  • The $y$-intercept is an important concept in mathematics and has many real-world applications.

Frequently Asked Questions

  • What is the $y$-intercept?
    • The $y$-intercept is the point on the line where $x$ is equal to zero.
  • How do I find the $y$-intercept of a linear equation?
    • To find the $y$-intercept, we need to substitute $x = 0$ into the equation and solve for $y$.
  • What is the $y$-intercept of the line $11x - 8y = -1$?
    • The $y$-intercept of the line $11x - 8y = -1$ is $\frac{1}{8}$.

References

Glossary

  • Linear Equation: An equation in which the highest power of the variable(s) is 1.
  • $y$-intercept: The point on the line where $x$ is equal to zero.
  • Substitute: To replace one value with another in an equation.
  • Solve: To find the value of a variable in an equation.
    Q&A: Finding the $y$-intercept of a Linear Equation =====================================================

Introduction

In our previous article, we learned how to find the $y$-intercept of a linear equation in the form $ax + by = c$. In this article, we will answer some frequently asked questions about finding the $y$-intercept of a linear equation.

Q: What is the $y$-intercept?

A: The $y$-intercept is the point on the line where $x$ is equal to zero. It is the value of $y$ when the line crosses the $y$-axis.

Q: How do I find the $y$-intercept of a linear equation?

A: To find the $y$-intercept, we need to substitute $x = 0$ into the equation and solve for $y$. This means that we need to replace $x$ with zero in the equation and simplify it to find the value of $y$.

Q: What is the $y$-intercept of the line $11x - 8y = -1$?

A: The $y$-intercept of the line $11x - 8y = -1$ is $\frac{1}{8}$. To find this, we need to substitute $x = 0$ into the equation and solve for $y$.

Step 1: Substitute $x = 0$ into the equation

11(0)−8y=−111(0) - 8y = -1

Step 2: Solve for $y$

−8y=−1-8y = -1

y=−1−8y = \frac{-1}{-8}

y=18y = \frac{1}{8}

Q: What if the equation is in the form $y = mx + b$?

A: If the equation is in the form $y = mx + b$, we can find the $y$-intercept by substituting $x = 0$ into the equation and solving for $y$. This means that we need to replace $x$ with zero in the equation and simplify it to find the value of $y$.

Example: Finding the $y$-intercept of the line $y = 2x + 3$

To find the $y$-intercept of the line $y = 2x + 3$, we need to substitute $x = 0$ into the equation and solve for $y$.

Step 1: Substitute $x = 0$ into the equation

y=2(0)+3y = 2(0) + 3

Step 2: Solve for $y$

y=3y = 3

Therefore, the $y$-intercept of the line $y = 2x + 3$ is $3$.

Q: What if the equation is in the form $ax + by = c$ and $a$ and $b$ are not integers?

A: If the equation is in the form $ax + by = c$ and $a$ and $b$ are not integers, we can still find the $y$-intercept by substituting $x = 0$ into the equation and solving for $y$. This means that we need to replace $x$ with zero in the equation and simplify it to find the value of $y$.

Example: Finding the $y$-intercept of the line $\frac{1}{2}x - \frac{3}{4}y = 2$

To find the $y$-intercept of the line $\frac{1}{2}x - \frac{3}{4}y = 2$, we need to substitute $x = 0$ into the equation and solve for $y$.

Step 1: Substitute $x = 0$ into the equation

12(0)−34y=2\frac{1}{2}(0) - \frac{3}{4}y = 2

Step 2: Solve for $y$

−34y=2-\frac{3}{4}y = 2

y=−2−34y = \frac{-2}{-\frac{3}{4}}

y=83y = \frac{8}{3}

Therefore, the $y$-intercept of the line $\frac{1}{2}x - \frac{3}{4}y = 2$ is $\frac{8}{3}$.

Conclusion

In this article, we answered some frequently asked questions about finding the $y$-intercept of a linear equation. We learned how to find the $y$-intercept of a linear equation in the form $ax + by = c$, and we also learned how to find the $y$-intercept of a linear equation in the form $y = mx + b$ and $ax + by = c$ where $a$ and $b$ are not integers.

Key Takeaways

  • The $y$-intercept is the point on the line where $x$ is equal to zero.
  • To find the $y$-intercept, we need to substitute $x = 0$ into the equation and solve for $y$.
  • The $y$-intercept is an important concept in mathematics and has many real-world applications.

Frequently Asked Questions

  • What is the $y$-intercept?
    • The $y$-intercept is the point on the line where $x$ is equal to zero.
  • How do I find the $y$-intercept of a linear equation?
    • To find the $y$-intercept, we need to substitute $x = 0$ into the equation and solve for $y$.
  • What is the $y$-intercept of the line $11x - 8y = -1$?
    • The $y$-intercept of the line $11x - 8y = -1$ is $\frac{1}{8}$.
  • What if the equation is in the form $y = mx + b$?
    • If the equation is in the form $y = mx + b$, we can find the $y$-intercept by substituting $x = 0$ into the equation and solving for $y$.
  • What if the equation is in the form $ax + by = c$ and $a$ and $b$ are not integers?
    • If the equation is in the form $ax + by = c$ and $a$ and $b$ are not integers, we can still find the $y$-intercept by substituting $x = 0$ into the equation and solving for $y$.

References

Glossary

  • Linear Equation: An equation in which the highest power of the variable(s) is 1.
  • $y$-intercept: The point on the line where $x$ is equal to zero.
  • Substitute: To replace one value with another in an equation.
  • Solve: To find the value of a variable in an equation.