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
