Damien Horton

2022-07-26

Write an equation of the line containing the given point and parallel to the given line.
(2,5);x+4y=5

Reinfarktq6

Expert

Given the equation: x+4y=5
4y= -x+5
y=(-1/4)x+(5/4)
Since the equation is parallel to the given line the slope(m)=-1/4
Given the point (2, 5) where ${x}_{1}=2,{y}_{1}=5$.
Use the point-slope formula:
$y-{y}_{1}=m\left(x-{x}_{1}\right)$
y-5=(-1/4)[x-2]
y=(-1/4)x+(1/2)+5
$y=-\frac{1}{4}x+\frac{11}{2}$... Equation of the line

Matilda Fox

Expert

the line: x+4y = 5 can be written as:
y = -(1/4)x + 5/4
the slop of the line is -1/4
for a line to be parallel with this line, its slop must be thesame as -1/4
the new line is y=mx+b = -(1/4)x + b
since it contains (2,5)
we have:
5=-(1/4)2 +b
b=5.5
y=-(1/4) x + 5.5 is the equation of the line

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