Question
Y=5x-4
What kind of solution does this have
What kind of solution does this have
Answers
Answered by
GPT-4o mini
The equation \( Y = 5x - 4 \) represents a linear equation in two variables (Y and x). It describes a straight line when graphed on a coordinate plane.
### Type of Solution:
1. **Infinite Solutions**: If you consider this equation in the context of a linear system (for example, when comparing with another line), the solutions can vary:
- If the second equation is identical to this one (for example, \( Y = 5x - 4 \)), there are infinitely many solutions (every point on the line).
- If the second equation is parallel to this one (e.g., \( Y = 5x + 1 \)), there are no solutions (the lines never intersect).
- If the second equation intersects this line at one point (for example, \( Y = -x + 1 \)), there is exactly one solution (the point where they intersect).
2. **Graphical Representation**: The equation \( Y = 5x - 4 \) can be graphed in the standard Cartesian coordinate system. The x-intercept can be found by setting \( Y = 0 \):
\[
0 = 5x - 4 \implies 5x = 4 \implies x = \frac{4}{5}.
\]
The y-intercept is at \( x = 0 \):
\[
Y = 5(0) - 4 \implies Y = -4.
\]
In conclusion, the type of solution it has depends on the context in which you are considering this equation (whether it's a stand-alone equation or part of a system of equations). As a single linear equation, it has an infinite number of solutions (all the points on the line itself).
### Type of Solution:
1. **Infinite Solutions**: If you consider this equation in the context of a linear system (for example, when comparing with another line), the solutions can vary:
- If the second equation is identical to this one (for example, \( Y = 5x - 4 \)), there are infinitely many solutions (every point on the line).
- If the second equation is parallel to this one (e.g., \( Y = 5x + 1 \)), there are no solutions (the lines never intersect).
- If the second equation intersects this line at one point (for example, \( Y = -x + 1 \)), there is exactly one solution (the point where they intersect).
2. **Graphical Representation**: The equation \( Y = 5x - 4 \) can be graphed in the standard Cartesian coordinate system. The x-intercept can be found by setting \( Y = 0 \):
\[
0 = 5x - 4 \implies 5x = 4 \implies x = \frac{4}{5}.
\]
The y-intercept is at \( x = 0 \):
\[
Y = 5(0) - 4 \implies Y = -4.
\]
In conclusion, the type of solution it has depends on the context in which you are considering this equation (whether it's a stand-alone equation or part of a system of equations). As a single linear equation, it has an infinite number of solutions (all the points on the line itself).