Substituting the Correct Value for y

Oct 13, 2025 by pinkandtrash.com 54 views

Understanding the Concept of ${$ x $}$ -intercept

The ${$ x$}$-intercept of a linear equation is the point at which the graph of the equation intersects the x-axis. At this point, the value of y is always zero. In other words, the ${$ x$}$-intercept is the solution to the equation when y is set to zero.

The Equation ${ $2x - 5y = 6\$}$ : A Closer Look

The given equation is ${ $2x - 5y = 6\$}$ . To find the ${$ x$}$-intercept, we need to substitute a value for y that will allow us to solve for x. The correct value to substitute for y is the one that will make the equation true when y is zero.

Substituting the Correct Value for y

To find the ${$ x$}$-intercept, we need to substitute y = 0 into the equation ${ $2x - 5y = 6\$}$ . This is because the ${$ x$}$-intercept occurs when y is zero.

Solving for x

When we substitute y = 0 into the equation, we get:

${ $2x - 5(0) = 6\$}$

Simplifying the equation, we get:

${ $2x = 6\$}$

Dividing both sides of the equation by 2, we get:

${$ x = 3$}$

Conclusion

Therefore, the value to substitute for y to find the ${$ x$}$-intercept of the equation ${ $2x - 5y = 6\$}$ is y = 0.

Why is y = 0 the Correct Value?

The reason why y = 0 is the correct value is that the ${$ x$}$-intercept occurs when the graph of the equation intersects the x-axis. At this point, the value of y is always zero. By substituting y = 0 into the equation, we are essentially finding the point at which the graph intersects the x-axis, which is the definition of the ${$ x$}$-intercept.

Common Mistakes to Avoid

One common mistake to avoid when finding the ${$ x$}$-intercept is to substitute a value for y that is not zero. For example, substituting y = 6 or y = -5 into the equation will not give us the correct value of x. This is because these values of y do not correspond to the ${$ x$}$-intercept.

Real-World Applications

Finding the ${$ x$}$-intercept has many real-world applications. For example, in physics, the ${$ x$}$-intercept can be used to find the point at which a projectile lands on the ground. In engineering, the ${$ x$}$-intercept can be used to find the point at which a beam or a column fails under load.

Conclusion

In conclusion, to find the ${$ x$}$-intercept of the equation ${ $2x - 5y = 6\$}$ , we need to substitute y = 0 into the equation. This is because the ${$ x$}$-intercept occurs when y is zero. By following this step-by-step guide, we can find the correct value of x and understand the concept of the ${$ x$}$-intercept.

Final Answer

The final answer is B. ${$ y = 0$}$.

Q: What is the ${$ x$}$-intercept of a linear equation?

A: The ${$ x$}$-intercept of a linear equation is the point at which the graph of the equation intersects the x-axis. At this point, the value of y is always zero.

Q: Why is y = 0 the correct value to substitute for y to find the ${$ x$}$-intercept?

A: The reason why y = 0 is the correct value is that the ${$ x$}$-intercept occurs when the graph of the equation intersects the x-axis. At this point, the value of y is always zero. By substituting y = 0 into the equation, we are essentially finding the point at which the graph intersects the x-axis, which is the definition of the ${$ x$}$-intercept.

Q: What happens if I substitute a value for y that is not zero?

A: If you substitute a value for y that is not zero, you will not get the correct value of x. This is because the value of y you substituted does not correspond to the ${$ x$}$-intercept.

Q: Can I use any value for y to find the ${$ x$}$-intercept?

A: No, you cannot use any value for y to find the ${$ x$}$-intercept. The only value you can use is y = 0, because this is the value that corresponds to the ${$ x$}$-intercept.

Q: How do I find the ${$ x$}$-intercept of a linear equation?

A: To find the ${$ x$}$-intercept of a linear equation, you need to substitute y = 0 into the equation and solve for x.

Q: What is the equation ${ $2x - 5y = 6\$}$ equal to when y = 0?

A: When y = 0, the equation ${ $2x - 5y = 6\$}$ becomes ${ $2x - 5(0) = 6\$}$ , which simplifies to ${ $2x = 6\$}$ .

Q: How do I solve for x in the equation ${ $2x = 6\$}$ ?

A: To solve for x, you need to divide both sides of the equation by 2, which gives you ${$ x = 3$}$.

Q: What is the ${$ x$}$-intercept of the equation ${ $2x - 5y = 6\$}$ ?

A: The ${$ x$}$-intercept of the equation ${ $2x - 5y = 6\$}$ is x = 3.

Q: Can I use the ${$ x$}$-intercept to find the value of y?

A: No, you cannot use the ${$ x$}$-intercept to find the value of y. The ${$ x$}$-intercept is the point at which the graph of the equation intersects the x-axis, and at this point, the value of y is always zero.

Q: What are some real-world applications of finding the ${$ x$}$-intercept?

A: Finding the ${$ x$}$-intercept has many real-world applications, such as finding the point at which a projectile lands on the ground in physics, or finding the point at which a beam or a column fails under load in engineering.

Q: Can I find the ${$ x$}$-intercept of a quadratic equation?

A: Yes, you can find the ${$ x$}$-intercept of a quadratic equation by substituting y = 0 into the equation and solving for x.

Q: How do I find the ${$ x$}$-intercept of a quadratic equation?

A: To find the ${$ x$}$-intercept of a quadratic equation, you need to substitute y = 0 into the equation and solve for x using the quadratic formula.

Q: What is the quadratic formula?

A: The quadratic formula is a mathematical formula that is used to solve quadratic equations. It is given by ${$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$}$.

Q: Can I use the quadratic formula to find the ${$ x$}$-intercept of a linear equation?

A: No, you cannot use the quadratic formula to find the ${$ x$}$-intercept of a linear equation. The quadratic formula is used to solve quadratic equations, not linear equations.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1, while a quadratic equation is an equation in which the highest power of the variable is 2.

Q: Can I find the ${$ x$}$-intercept of a cubic equation?

A: Yes, you can find the ${$ x$}$-intercept of a cubic equation by substituting y = 0 into the equation and solving for x.

Q: How do I find the ${$ x$}$-intercept of a cubic equation?

A: To find the ${$ x$}$-intercept of a cubic equation, you need to substitute y = 0 into the equation and solve for x using the cubic formula.

Q: What is the cubic formula?

A: The cubic formula is a mathematical formula that is used to solve cubic equations. It is given by ${$ x = \frac{-b \pm \sqrt{b^2 - 3ac}}{3a}$}$.

Q: Can I use the cubic formula to find the ${$ x$}$-intercept of a linear equation?

A: No, you cannot use the cubic formula to find the ${$ x$}$-intercept of a linear equation. The cubic formula is used to solve cubic equations, not linear equations.

Q: What is the difference between a linear equation, a quadratic equation, and a cubic equation?

A: A linear equation is an equation in which the highest power of the variable is 1, a quadratic equation is an equation in which the highest power of the variable is 2, and a cubic equation is an equation in which the highest power of the variable is 3.