The y-intercept of a line is the point where the line crosses the y-axis. It is represented by the value of y when x is equal to 0. In simpler terms, it's the point on the graph where the line touches the vertical axis....
Finding the y-intercept
To find the y-intercept of a line, we can use the following steps:
- Set x to 0 in the equation of the line.
- Solve for y.
Applying the method to 3y = x
Let's follow the steps to find the y-intercept of the line 3y = x:
- Set x to 0: 3y = 0
- Solve for y: y = 0 / 3 = 0
Conclusion
Therefore, the y-intercept of the line 3y = x is 0. So the statement "The y-intercept of the line 3y = x is 0" is **TRUE**.
Additional Considerations
Here are some additional things to keep in mind when determining y-intercepts:
- Slope-intercept form: The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. If the equation is already in this form, the y-intercept is directly identifiable as the value of 'b'.
- Graphing: You can also determine the y-intercept by graphing the line. The point where the line intersects the y-axis represents the y-intercept.
Example
Let's look at another example to solidify the concept. Consider the line y = 2x + 3.
- Slope-intercept form: The equation is already in slope-intercept form. We can directly identify the y-intercept as 3.
- Setting x to 0: If we substitute x = 0 into the equation, we get y = 2(0) + 3, which simplifies to y = 3. This confirms that the y-intercept is 3.
- Graphing: When graphing the line, you'll observe that it intersects the y-axis at the point (0, 3), again confirming the y-intercept is 3.
By understanding these concepts and methods, you can confidently determine the y-intercept of any linear equation.