write the general forms of the equations of the lines that pass through the point and are (a) parallel to the given line and (b) perpendicular to the given line. (3/4, 7/8) 5x−3y=0

Reeves

Reeves

Answered question

2021-01-31

write the general forms of the equations of the lines that pass through the point and are (a) parallel to the given line and (b) perpendicular to the given line.
(34,78)5x3y=0

Answer & Explanation

Sadie Eaton

Sadie Eaton

Skilled2021-02-01Added 104 answers

Given point and equation of line
(34,78)
5x3y=0
We need to find the equation of line which is
a) Parallel to the given line.
b) Perpendicular to the given line.
Concept:
When two lines are parallel then, the slope of the lines are equal.
When two lines are perpendicular then, the product of the slope of the lines is equal to –1.
The equation of the line with point (x’, y’) and slope m is given below:
yy=m(xx)
The slope of the given line can be calculated by finding the derivative of the given equation:
5x3y=0
53dydx=0
m2=dydx=53
a) Equation of line which is parallel to the given equation of line and passes through the given point (34,78).
m1=m2=53
yy=m1(xx)
y78=53(x34)
y=5x354+78
5x338
y=53x38
b) Equation of line which is perpendicular to the given equation of line and passes through the given point (34,78).
m1×m2=1
m1×(53)=1
m1=35
yy=m1(xx)
y78=35(x34)
y=35x+920+78
y=35x+18+3540
Y=35x+5340
a)PARALLEL
b)PERPENDICULAR

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