Answer:
5x +3y = -14
Explanation:
The equation of the given line is in standard form. This makes it easy to write the equation for a perpendicular line.
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form
The perpendicular line will have a slope that is the negative reciprocal of the slope of the given line. This can be made to happen by ...
- swapping the coefficients of x- and y
- negating one of the coefficients.
So, the line perpendicular to 3x -5y = 2 will have an equation of the form ...
5x +3y = c . . . . . for some constant c
constant
The constant will be what is needed to make the line go through the given point. That is, for (x, y) = (-1, -3), the equation is satisfied.
5(-1) +3(-3) = c = -5 -9 = -14 . . . . . substitute values for x and y
equation
Then the equation for the perpendicular line through (-1, -3) is ...
5x +3y = -14