Question

the equation of line k is $y = -x + 17$. line n is parallel to line k and passes through the point $(-5, 7)$. determine an equation that represents the relationship between x and y for line n. enter your answer in the space provided.

Explanation:

Step1: Determine the slope of line n

Parallel lines have the same slope. The equation of line \( k \) is \( y = -x + 17 \), which is in slope - intercept form \( y=mx + b \) (where \( m \) is the slope and \( b \) is the y - intercept). For the line \( y=-x + 17 \), the slope \( m=- 1 \). So the slope of line \( n \), \( m_{n}=-1 \).

Step2: Use the point - slope form to find the equation of line n

The point - slope form of a line is \( y - y_{1}=m(x - x_{1}) \), where \( (x_{1},y_{1}) \) is a point on the line and \( m \) is the slope. We know that line \( n \) passes through the point \( (-5,7) \), so \( x_{1}=-5 \), \( y_{1}=7 \) and \( m=-1 \).
Substitute these values into the point - slope form:
\( y - 7=-1(x - (-5)) \)
Simplify the right - hand side: \( y - 7=-1(x + 5) \)
Expand the right - hand side: \( y - 7=-x - 5 \)
Add 7 to both sides of the equation to get it into slope - intercept form:
\( y=-x - 5+7 \)
\( y=-x + 2 \)

Answer:

\( y=-x + 2 \)