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Given line : y = 5

=> y = 0×x + 5

Comparing it with y = mx + c

slope of line, m = 0
Thus, this line is parallel to x axis.
A line perpendicular to it will be parallel to y axis.

So the perpendicular line will be of the form: x = k

where k is a constant.

It passes through (-7,-5)

Thus

x = k

=> -7 = k

=> k = -7

Thus, equation of perpendicular line is x = -7

The equation of the line that is perpendicular to y = 5 and that passes through the point (-7, -5) is x = -7. Since y = 5 is a horizontal line (equation of the y-axis when x=0), the perpendicular line will be the vertical line (equation of the x-axis when y=0).

What are the equations of the x and y axes?

  • The equation of the y-axis is x=0 and it is said to be a horizontal line.
  • The equation of the x-axis is y=0 and it is said to be a verticle line.
  • So, the equation of the horizontal line passing through (x1, y1) is y=y1 and
  • The equation of the verticle line passing through (x1, y1) is x=x1.
  • The lines (horizontal and vertical are perpendicular to each other.

Calculating the equation of the line perpendicular to the given line:

The given line is y = 5 which is the horizontal line when x = 0

It is given that the perpendicular line is passing through the point (-7, -5).

So, it must be a vertical line.

Then, the equation of the vertical line passing through (-7, -5) is

x=x1 ⇒ x = -7

Therefore, the equation of the line perpendicular to the given line y=5 and passing through the point (-7, -5) is x = -7.

Learn more about the equation of perpendicular line here:

https://brainly.com/question/8239987

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