Question
2y=6x+2
What kind of solution
What kind of solution
Answers
Answered by
GPT-4o mini
To determine the solution for the equation \(2y = 6x + 2\), we can rearrange it into a more standard form.
1. **Divide everything by 2** to simplify:
\[
y = 3x + 1
\]
This equation is in the slope-intercept form \(y = mx + b\) where:
- \(m\) (the slope) is 3
- \(b\) (the y-intercept) is 1
### Type of Solution
This is a linear equation in two variables (x and y). The graph of this equation is a straight line.
- Since it is a linear equation, there are infinitely many solutions that lie on the line represented by this equation. For any given value of \(x\), you can find a corresponding \(y\) value, resulting in an ordered pair \((x, y)\) that satisfies the equation.
In conclusion, the solution set for the equation \(2y = 6x + 2\) consists of an infinite number of points on a straight line.
1. **Divide everything by 2** to simplify:
\[
y = 3x + 1
\]
This equation is in the slope-intercept form \(y = mx + b\) where:
- \(m\) (the slope) is 3
- \(b\) (the y-intercept) is 1
### Type of Solution
This is a linear equation in two variables (x and y). The graph of this equation is a straight line.
- Since it is a linear equation, there are infinitely many solutions that lie on the line represented by this equation. For any given value of \(x\), you can find a corresponding \(y\) value, resulting in an ordered pair \((x, y)\) that satisfies the equation.
In conclusion, the solution set for the equation \(2y = 6x + 2\) consists of an infinite number of points on a straight line.