Questions: through: (-2,2), parallel to y=x+1

through: (-2,2), parallel to y=x+1
Transcript text: through: $(-2,2)$, parallel to $y=x+1$
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Solution

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Solution Steps

To find the equation of a line that passes through a given point and is parallel to a given line, we need to use the slope of the given line. Since parallel lines have the same slope, we can use the slope of the line \( y = x + 1 \), which is 1. Then, we use the point-slope form of a line equation, \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \((x_1, y_1)\) is the given point.

Step 1: Determine the Slope

The slope \( m \) of the line given by the equation \( y = x + 1 \) is \( 1 \). Since we are looking for a line that is parallel to this line, it will also have the same slope.

Step 2: Use the Point-Slope Form

We have the point \( (-2, 2) \) through which the line passes. Using the point-slope form of the line equation:

\[ y - y_1 = m(x - x_1) \]

Substituting \( m = 1 \), \( x_1 = -2 \), and \( y_1 = 2 \):

\[ y - 2 = 1(x + 2) \]

Step 3: Rearrange to Slope-Intercept Form

Rearranging the equation gives us:

\[ y - 2 = x + 2 \]

Adding \( 2 \) to both sides results in:

\[ y = x + 4 \]

Final Answer

The equation of the line that passes through the point \( (-2, 2) \) and is parallel to \( y = x + 1 \) is

\[ \boxed{y = x + 4} \]

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