The equation of the line will be 3y + 8x = 165.
<h3>What is an equation?</h3>
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that:-
- Find the equation of the line through point (8,−9) ( 8, − 9 ) and perpendicular to 3 x + 8 y = 4.
The given equation of the line is:-
3 x + 8 y = 4.
The slope of this line will be:-
3 x + 8 y = 4.
8y = -3x + 4
y = -3 /8x + ( 1 / 2)
y = mx + c
m = -3 / 8
Since the line is perpendicular to the other line 3x +8y = 4 so the slope will be inverse and negative for the line.
So the slope of the line will be -8 / 3
The equation of the line passing through the point will be given as:-
y - y 1 = m ( x- x1)
y - (-9) = ( -8 / 3) ( x - 8)
Y + 9 = ( -8 / 3 ) ( x -8 )
3 y = -8x + 165
3y + 8x = 165
Therefore the equation of the line will be 3y + 8x = 165.
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