The { X$}$-intercept Of The Line Whose Equation Is { Y = 5x - 10$}$ Is:A. 2 B. { -10$}$ C. 5

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Understanding the Concept of $x$-intercept

The $x$-intercept of a line is the point at which the line intersects the $x$-axis. In other words, it is the point where the line crosses the $x$-axis, and the $y$-coordinate is always zero. To find the $x$-intercept of a line, we need to set the $y$-coordinate to zero and solve for the $x$-coordinate.

Finding the $x$-intercept of the Line $y = 5x - 10$

To find the $x$-intercept of the line $y = 5x - 10$, we need to set the $y$-coordinate to zero and solve for the $x$-coordinate. This can be done by substituting $y = 0$ into the equation and solving for $x$.

y = 5x - 10
0 = 5x - 10
5x = 10
x = 10/5
x = 2

Therefore, the $x$-intercept of the line $y = 5x - 10$ is $x = 2$.

Conclusion

In conclusion, the $x$-intercept of the line whose equation is $y = 5x - 10$ is $x = 2$. This means that the line intersects the $x$-axis at the point $(2, 0)$.

Example Problems

Problem 1

Find the $x$-intercept of the line whose equation is $y = 3x + 2$.

Solution

To find the $x$-intercept of the line $y = 3x + 2$, we need to set the $y$-coordinate to zero and solve for the $x$-coordinate.

y = 3x + 2
0 = 3x + 2
3x = -2
x = -2/3
x = -\frac{2}{3}

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

Problem 2

Find the $x$-intercept of the line whose equation is $y = 2x - 4$.

Solution

To find the $x$-intercept of the line $y = 2x - 4$, we need to set the $y$-coordinate to zero and solve for the $x$-coordinate.

y = 2x - 4
0 = 2x - 4
2x = 4
x = 4/2
x = 2

Therefore, the $x$-intercept of the line $y = 2x - 4$ is $x = 2$.

Applications of $x$-intercept

The $x$-intercept of a line has many applications in real-life situations. For example, in physics, the $x$-intercept of a line can represent the point at which a projectile lands on the ground. In economics, the $x$-intercept of a line can represent the point at which a company's revenue equals its cost.

Conclusion

In conclusion, the $x$-intercept of a line is an important concept in mathematics that has many applications in real-life situations. By understanding how to find the $x$-intercept of a line, we can solve many problems in physics, economics, and other fields.

Final Answer

The final answer is: $\boxed{2}$

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Understanding the Concept of $x$-intercept

The $x$-intercept of a line is the point at which the line intersects the $x$-axis. In other words, it is the point where the line crosses the $x$-axis, and the $y$-coordinate is always zero. To find the $x$-intercept of a line, we need to set the $y$-coordinate to zero and solve for the $x$-coordinate.

Q&A

Q: What is the $x$-intercept of the line $y = 5x - 10$?

A: The $x$-intercept of the line $y = 5x - 10$ is $x = 2$.

Q: How do I find the $x$-intercept of a line?

A: To find the $x$-intercept of a line, you need to set the $y$-coordinate to zero and solve for the $x$-coordinate.

Q: What is the $x$-intercept of the line $y = 3x + 2$?

A: The $x$-intercept of the line $y = 3x + 2$ is $x = -\frac{2}{3}$.

Q: What is the $x$-intercept of the line $y = 2x - 4$?

A: The $x$-intercept of the line $y = 2x - 4$ is $x = 2$.

Q: What is the significance of the $x$-intercept of a line?

A: The $x$-intercept of a line has many applications in real-life situations, such as in physics, economics, and other fields.

Q: How do I use the $x$-intercept of a line in real-life situations?

A: The $x$-intercept of a line can be used to represent the point at which a projectile lands on the ground, or the point at which a company's revenue equals its cost.

Example Problems with Solutions

Problem 1

Find the $x$-intercept of the line whose equation is $y = 4x - 6$.

Solution

To find the $x$-intercept of the line $y = 4x - 6$, we need to set the $y$-coordinate to zero and solve for the $x$-coordinate.

y = 4x - 6
0 = 4x - 6
4x = 6
x = 6/4
x = 3/2

Therefore, the $x$-intercept of the line $y = 4x - 6$ is $x = \frac{3}{2}$.

Problem 2

Find the $x$-intercept of the line whose equation is $y = x + 1$.

Solution

To find the $x$-intercept of the line $y = x + 1$, we need to set the $y$-coordinate to zero and solve for the $x$-coordinate.

y = x + 1
0 = x + 1
x = -1

Therefore, the $x$-intercept of the line $y = x + 1$ is $x = -1$.

Conclusion

In conclusion, the $x$-intercept of a line is an important concept in mathematics that has many applications in real-life situations. By understanding how to find the $x$-intercept of a line, we can solve many problems in physics, economics, and other fields.

Final Answer

The final answer is: $\boxed{2}$