The equation of the perpendicular line is:
y = (-1/13)*x - 87/13
How to get the line equation?
For a general linear equation:
y = a*x + b
Another linear equation that is perpendicular to the above one is given by:
y = (-1/a)*x + c
Where a, b, and c are real numbers.
In this case, we want to find a perpendicular line to:
y = 13*x - 2
Then it will be something like:
y = (-1/13)*x + c
To find the value of c, we use the fact that it must pass through the point (4, -7), then:
-7 = (-1/13)*4 + c
Now we can solve that for c:
-7 + 4/13 = c
-87/13
Then the linear equation is:
y = (-1/13)*x - 87/13
If you want to learn more about linear equations:
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