To find the slope and y-intercept of the equation \( -6x + 3y = 46 \) that has infinite solutions, we first need to rewrite the equation in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Starting with the original equation:
\[ -6x + 3y = 46 \]
We will solve for \( y \):
- Add \( 6x \) to both sides:
\[ 3y = 6x + 46 \]
- Divide each term by \( 3 \):
\[ y = 2x + \frac{46}{3} \]
Now we can identify the slope and y-intercept:
- The slope \( m \) is \( 2 \).
- The y-intercept \( b \) is \( \frac{46}{3} \).
Thus:
- The slope would be \( 2 \).
- The y-intercept would be \( \frac{46}{3} \).
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