On solving the provided question, an equation of the line that passes through the point (-7,0)(−7,0) and is parallel to the line [tex]xy=1[/tex], answer is - [tex]y = -x - 7[/tex]
Parallel lines in geometry are coplanar, straight lines that don't cross at any point. Planes that never cross each other in the same three-dimensional space are said to be parallel. Curves that maintain a fixed minimum distance and do not touch or intersect are said to be parallel curves. Parallel lines are those that, when stretched in a plane, do not intersect. Since parallel lines never cross, their separation always remains the same.
Two lines with the same slope are parallel to one another.
x + y = 1 appears on the first line.
Let's first convert this to standard form.
[tex]x + y = 1\\y = -x + 1[/tex]
The equation is now in standard form. It has a -1 slope. This line's parallel will also have a -1 slope.
In your conventional point-slope equation of y = mx + b, plug in this number (-1).
[tex]y = -x + b[/tex]
The value that we know is on this line, in this case it is, should be plugged in to find b. (-7, 0). Put the values of x and y into the x and y of the common equation.
[tex]0 = -1(-7) + b[/tex]
[tex]0 = 7 + b[/tex]
[tex]-7 = b[/tex]
[tex]y = -x - 7[/tex]
This equation comprises point and is parallel to the one you provided (y = -x + 1). (-7, 0)
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