Answer :
The equation of a line that is parallel to 4x+3y=12 and passes through the point (3, 4) is 4x+3y = 24
The standard form of equation of line is y=m x+ b
where m is slope of line and b is y-intercept.
According to the question,
The required line is parallel to line whose equation is 4x + 3y = 12
Slope of given line =
3y = 12 - 4x
dividing by 3 both sides,
y = 12/3 - 4/3x
=> y = 4 - 4/3x
Slope of given line = -4/3
If two lines are parallel their slopes are equal to each other
Hence , Slope of required line : m = -4/3
Equation of line : y = -4/3x + b ------------(1)
It is given that required line also passes through the point = (3,4)
substituting the values of x = 3 and y=4 in equation (1)
=> (4) = (-4/3)(3) + b
=> 4 = -4 +b
=> b = 8
Substituting the value of b,
The equation of required line is y = -4/3x + 8
multiplying by 3 both sides,
3y = -4x + 24
=> 4x+3y = 24
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