Question

What is an equation of the line that passes through the point (-6,-4) and is parallel to the line 3y=2x-6

Answer 1

y =
`(2)/(3)`x

Step-by-step explanation:

Given parameters:

Coordinates = (-6, -4)

Equation of a the line; 3y = 2x - 6

Unknown:

Equation of the line parallel to this line = ?

Solution:

The equation of any straight line is expressed as;

y = mx + c

y and x are the coordinate

m is the slope

c is the intercept of the y - axis

Now from the equation, let us find the slope;

3y = 2x - 6

y =
`(2)/(3) x` -
`(6)/(3)`

y =
`(2)/(3) x` - 2

The slope is
`(2)/(3)`

Parallel lines are lines that never meets. Therefore they have the same slope;

the slope of the new line is
`(2)/(3)`

Now,

for the new line, we need to find the intercept;

since y = mx + c,

y = -4 and x = -6;

-4 =
`(2)/(3)` x (-6) + c

- 4 = -4 + c

c= 0

The equation of the new line is;

y =
`(2)/(3)`x