To find the slope-intercept form of the equation of a line that is parallel to another line and passes through a specific point, we first need the slope of the original line.
Since the original line's equation isn’t given explicitly in your message, let's assume that the equation of the line being referred to is given as \( y = mx + b \), where \( m \) is the slope.
Steps to find the equation of the parallel line:
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Determine the slope of the original line: If the original line's equation is something recognizable (e.g., \( y = 2x + 1 \)), let's say it has a slope of \( m = 2 \). If you have the specific equation, you can identify its slope.
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Use the point-slope formula: Since we want a line parallel to the original line, it will have the same slope.
We can apply the point-slope formula, which is given by: \[ y - y_1 = m(x - x_1) \] where \((x_1, y_1)\) is the point the line passes through—in this case, (3, 3).
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Insert the point and slope:
- Using \( m \) (from the original line) and the point (3, 3): \[ y - 3 = m(x - 3) \]
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Convert it to slope-intercept form: Solve for \( y \) to put it in the form \( y = mx + b \).
Example:
Assuming the slope of the line is \( m = 2 \) (if the original line is \( y = 2x + b \)): \[ y - 3 = 2(x - 3) \] Expanding this gives: \[ y - 3 = 2x - 6 \] \[ y = 2x - 3 \]
So, the slope-intercept form of the line parallel to the original line and passing through the point (3, 3) would be \( y = 2x - 3 \).
If you have the original line's equation, replace \( m \) with that slope to find your final answer.