Question

Write an equation that is parallel to the line 2x - 3y = 9 and passes through the point (4, -1).
A) y =
2
3
x -
11
3
B) y =
3
2
x -
11
3
C) y =
2
3
x +
11
3
D) y = −
2
3
x -
11
3

Answer 1

Answer: $y = \frac{2x}{3} - \frac{11}{3}$

Step-by-step explanation:

Equation of the line given ;

$2x - 3y = 9$

To find the slope of the line we will make y the subject of formula , that is

$3y = 2x - 9$

$y = \frac{2x}{3}-3$

Therefore ; the slope = $\frac{2}{3}$

Two lines are said to be parallel if they have the same slope

This means that the slope of the second line = $\frac{2}{3}$

Using the formula $y-y_{1}= m ( x - x_{1} )$ to find the equation of the line , we have

$y - (-1 ) = \frac{2}{3} (x - 4 )$

$y + 1 = \frac{2x}{3} -\frac{2}{3}(4)$

$y + 1 = \frac{2x}{3} - \frac{8}{3}$

$y = \frac{2x}{3}- \frac{8}{3} - 1$

$y = \frac{2x}{3} - \frac{11}{3}$