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Find the equation of the line which passes through (6,2) and is parallel to the line with equation 3y=5x+2

Sagot :

Answer:

Step-by-step explanation:

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Answer:

3y = 5x - 24

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

3y = 5x + 2 ( divide through by 3 )

y = [tex]\frac{5}{3}[/tex] x + [tex]\frac{2}{3}[/tex] ← in slope- intercept form

with slope m = [tex]\frac{5}{3}[/tex]

• Parallel lines have equal slopes , then

y = [tex]\frac{5}{3}[/tex] x + c ← is the partial equation of the parallel line

to find c substitute (6, 2 ) into the partial equation

2 = 10 + c ⇒ c = 2 - 10 = - 8

y = [tex]\frac{5}{3}[/tex] x - 8 ← equation in slope- intercept form

multiply through by 3 to clear the fraction

3y = 5x - 24 ← equation of parallel line

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