Write an equation of a line parallel to line GH below in slope-intercept form that passes through the point $(-5,6)$.
A. $y=-x-1$
B. $y=x-1$
C. $y=-x+11$
D. $y=x+11$
Answer (2)
Determine the slope of the given line: m = − 1 .
Use the point-slope form with the given point ( − 5 , 6 ) and slope m = − 1 : y − 6 = − 1 ( x + 5 ) .
Convert to slope-intercept form: y = − x + 1 .
The equation of the line is y = − x + 1 .
Explanation
Understanding the Problem We are given the equation of a line y = − x − 1 and asked to find the equation of a line parallel to it that passes through the point ( − 5 , 6 ) . Parallel lines have the same slope. We will use this fact to find the equation of the desired line.
Finding the Slope The given line is in slope-intercept form, y = m x + b , where m is the slope and b is the y-intercept. For the line y = − x − 1 , the slope is m = − 1 .
Using Point-Slope Form Since the line we want to find is parallel to the given line, it will have the same slope, m = − 1 . We also know that the line passes through the point ( − 5 , 6 ) . We can use the point-slope form of a line, which is y − y 1 = m ( x − x 1 ) , where ( x 1 , y 1 ) is a point on the line and m is the slope.
Substituting Values Substituting the point ( − 5 , 6 ) and the slope m = − 1 into the point-slope form, we get:
y − 6 = − 1 ( x − ( − 5 ))
y − 6 = − 1 ( x + 5 )
Converting to Slope-Intercept Form Now, we convert the equation to slope-intercept form, y = m x + b , by solving for y :
y − 6 = − x − 5
y = − x − 5 + 6
y = − x + 1
Final Answer Therefore, the equation of the line parallel to y = − x − 1 that passes through the point ( − 5 , 6 ) is y = − x + 1 .
Examples
Understanding parallel lines is crucial in architecture and design. For example, when designing a building, architects use parallel lines to ensure walls are aligned and structures are stable. If a wall needs to be parallel to another for aesthetic or structural reasons, the principles used in this problem apply directly to ensure the correct alignment and design.
The equation of a line parallel to line GH that passes through the point ( − 5 , 6 ) is y = − x + 1 . However, this specific equation does not match any of the provided options. Thus, the answer to the question based on our calculations is clear even if the options are not correct.
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