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Lines l and M are parallel. Line l can be represented by the equation 3x+4y=8. If line m passes through the point (2, -5), which equation can be used to find the equation of line m?

Respuesta :

abidemiokin

Answer:

3y - 4x + 7 = 0

Step-by-step explanation

The equation of the line l in point slope form is expressed as;

y-y0 = m(x-x0)

Get the slope m of the known line

Given the line 3x+4y=8

4y = -3x+8

y = -3x/4 + 2

m = -3/4

The slope of the line m = -1/(-3/4) = 4/3

Substitute m = 4/3 and the point (2,-5) into the expression above;

y - (-5) = 4/3(x-2)

y+5 = 4/3 x + 8/3

Multiply through by 3;

3y + 15 = 4x + 8

3y-4x + 15 - 8 = 0

3y - 4x + 7 = 0

Hence the equation that can be used to find the equation of line m is 3y - 4x + 7 = 0

Equation that can be used to find the equation of line m is

[tex]y+5=\frac{-3}{4} (x-2)[/tex]

Given :

Lines l and M are parallel. Line l can be represented by the equation 3x+4y=8

Line m passes through the point (2, -5)

Equation of line L is [tex]3x+4y=8[/tex]

Lets find out the slope of the given equation by writing it in y=mx+b form

where m is the slope

[tex]3x+4y=8\\4y=-3x+8\\y=\frac{-3}{4}x +2[/tex]

the slope of line L is [tex]\frac{-3}{4}[/tex]

Slope of parallel lines are equal

slope of parallel line M is also [tex]\frac{-3}{4}[/tex]

Line M passes through (2,-5)

We use point slope formula to find equation of line m

[tex]y-y_1=m(x-x_1)\\y+5=\frac{-3}{4} (x-2)\\[/tex]

Multiply both sides by 4

[tex]4(y+5)=-3 (x-2)\\4y+20=-3x+6\\3x+4y+20=6\\3x+4y=14[/tex]

equation can be used to find the equation of line  is

[tex]y+5=\frac{-3}{4} (x-2)[/tex]

Learn more :  brainly.com/question/19729250

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