## 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

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

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