Question

Find the equation of the line. A line that is parallel to the graph of 2x+3y=5 and contains the point (3,-1).

Answer 1

Step-by-step explanation:

topic :

• slope and point

given :

• line that is parallel to the graph = 2x+3y=5

• contains point = (3,-1).

to find :

• Find the equation of the line = ?

• Find the equation of the line = ?

solution :

• line = 2x + 3y = 5

• line = -2/3

• line passing through = (3 , -1)

• line is parallel = (m1) × (m2) = - 1

• slop of 2 line = -1/m1

• = -1(-2/3)

• = 3/2

• equal of line = (3 , -1) slope

• Y-y1 = (m2)(x-x1)

• 2Y +2= 3X - 9

• line of equation = 3X - 2Y = 11

• point = (5,6) s (3, 4)

• = y2- y1 / x 2 - x1 = 4 -6 /3-5 = 1

• line of equation = Y=X+1

• points = (0,7), (0, -8)

• coordinates = y2 - y1 / x 2 - X1

• = -8 -7/ 0-0

• = 0

• line of equation = 3

thus, the answer 2x + 3y = 3

Answer 2

GIVEN :–

• Required line parallel to 2x + 3y = 5.

• Required line contains the point (3,-1).

TO FIND :–

• Equation of line = ?

SOLUTION :–

• We know that parallel lines have equal slope.

• Now let the slope of given line is M₁ and slope of required line is M₂

➪ M₁ = - [Coefficient of x]/[Coefficient of y]

➪ M₁ = - ⅔

[ ∵ M₁ = M₂ ]

➪ M₂ = - ⅔

• Point slope form of line –

⇛ y - b = M ( x - a )

★ Here –

▪︎ M = slope

▪︎ a = 3

▪︎ b = -1

• According to the question –

➪ y - (-1) = [-⅔] ( x - 3 )

➪ y + 1 = (-⅔)(x - 3)

➪ (y + 1)3 = -2(x - 3)

➪ 3y + 3 = -2x + 6

➪ 2x + 3y = 3

• Hence , Required line is 2x + 3y = 3.