find the equation of a line that is parallel to the line x= -1 and contains the point (-7,5)
the equation of the parallel line is ?
*type an equation*
x=-1 is a vertical line
so the line through (-7,5) is a vertical line
easy to find, just set x equal to the x of the point
so
x = -7
To find the equation of a line parallel to the line x = -1, we need to determine the equation in the form of y = mx + b.
Since the line x = -1 is a vertical line, its slope is undefined (or infinite). Therefore, any line parallel to x = -1 will also have an undefined slope.
Now, to find the equation of the parallel line that passes through the point (-7, 5), we can use the point-slope form.
The point-slope form is given by: y - y1 = m(x - x1)
Where (x1, y1) are the coordinates of the given point, and m is the slope.
However, since the slope is undefined in this case, we write the equation in terms of x.
Using the given point (-7, 5), we substitute x1 = -7 and y1 = 5 into the equation:
y - 5 = undefined * (x - (-7))
Simplifying:
y - 5 = undefined * (x + 7)
Since the slope is undefined, we can simplify to:
y - 5 = undefined
Finally, rewriting undefined as 1/0 since division by zero is undefined:
y - 5 = 1/0
We cannot have a denominator of zero in an equation, so we conclude that the equation of the parallel line is simply:
y = 5
Hence, the equation of the parallel line is y = 5.