Answer:
Step-by-step explanation:
To find its slope, put 3x+8y=4 into slope-intercept form.
y= -3/8x + 1/2
We know that since the lines are perpendicular, the slope of the new line will be the negative reciprocal of the old line's slope.
m = 8/3
Now we plug in our new slope and our given point into the point-slope formula.
y-(-9) = 8/3(x-8)
All that is left to do is to put our equation into slope intercept form.
y = 8/3x-37/3
HTH :)
The equation of the given straight line through the point (8,−9) and perpendicular to 3x+8y=4 is 8x - 3y = 91.
We know that the equation of any straight line is y = mx + c, where m denotes the slope and c denotes a constant.
In addition, the slopes of two perpendicular lines are the negative reciprocals of one another.
Here, the equation of the given straight line is
3x+8y=4
i.e. 8y = 4 -3x
i.e. y = (4/8) - (3/8)x
Now the negative reciprocal of - 3/8 is 8/3.
Then we can write the equation of the perpendicular line is
y = (8/3)x + c ...(1)
Since (1) passes through the point (8, -9), so we can put x = 8 and y = -9 in (1) to get the value of c.
So, -9 = (8/3)*8 + c
i.e. -9 = 64/3 + c
i.e. c = -9 -64/3 = - (27 + 64)/3 = - 91/3
(1) can be written as
y = (8/3)x - (91/3)
i.e. 3y = 8x - 91
i.e. 8x - 3y = 91
Therefore the equation of the line through the point (8,−9) and perpendicular to 3x+8y=4 is given by 8x - 3y = 91.
Learn more about perpendicular lines here -
brainly.com/question/12209021
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