Write the equation of a line that is parallel to the line 2x – 3y = 5 and passes through the point (2, -1) A. 2x-3y=7 B. 3

Question

Write the equation of a line that is parallel to the line 2x – 3y = 5 and passes through the point (2, -1)

A. 2x-3y=7
B. 3x+2y=5
C. 3x-2y=7
D. 2x+3y=1

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Savannah 2 weeks 2021-11-21T23:32:43+00:00 1 Answer 0

Answers ( )

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    2021-11-21T23:33:47+00:00

    Answer:

    The equation of the line is 2x – 3y = 7 ⇒ answer A

    Step-by-step explanation:

    * Lets revise the relation between the parallel lines

    – If two lines are equal then their slopes are equal

    – We can make an equation of a line by using its slope and

     a point on the line

    – If the slope of the line is m and passing through the point (x1 , y1),

     then we can use this form [y – y1]/[x – x1] = m to find the equation

    * Lets solve the problem

    – The line is parallel to the line 2x – 3y = 5

    ∴ the slope of the line = the slope of the line 2x – 3y = 5

    – Rearrange the terms of the equation to be in the form

      y = mx + c to find the slope of it

    ∵ 2x – 3y = 5 ⇒ subtract 2x from both sides

    ∴ -3y = 5 – 2x ⇒ divide two sides by -3

    ∴ y = 5/-3 – 2x/-3 ⇒ y = 2/3 x – 5/3

    ∴ The slop of the line is 2/3

    ∵ The line passes through point (2 , -1)

    * Lets use the rule to find the equation of the line

    ∵ y – (-1)/x – 2 = 2/3

    ∴ y + 1/x – 2 = 2/3 ⇒ by using cross multiplication

    ∴ 3(y + 1) = 2(x – 2) ⇒ open the brackets

    ∴ 3y + 3 = 2x – 4 ⇒ put x an d y in one side

    ∴ 2x – 3y = 3 + 4

    ∴ 2x – 3y = 7

    * The equation of the line is 2x – 3y = 7

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