To find the equation of a line that is parallel to a given line and passes through a specific point, we need to follow these steps:
- Identify the slope of the given line.
- Use that slope to write the equation of the new line in point-slope form using the given point.
The equation of the given line is:
\[ y = 2x + 7 \]
From this equation, we can see that the slope (m) is 2.
Since parallel lines have the same slope, the slope of the new line will also be 2.
Now, we can use the point-slope form of the equation of a line, which is given by:
\[ y - y_1 = m(x - x_1) \]
Where \((x_1, y_1)\) is the given point and \(m\) is the slope. Here \((x_1, y_1) = (3, 11)\) and \(m = 2\).
Substituting these values into the point-slope equation:
\[ y - 11 = 2(x - 3) \]
Now, we can simplify this equation:
\[ y - 11 = 2x - 6 \]
Adding 11 to both sides to solve for \(y\):
\[ y = 2x - 6 + 11 \] \[ y = 2x + 5 \]
So, the equation of the line that is parallel to the given line and passes through the point (3, 11) is:
\[ y = 2x + 5 \]
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