Answer:
y = [tex]\frac{2}{3}[/tex]x
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 = [tex]\frac{2}{3} x[/tex] - [tex]\frac{6}{3}[/tex]
y = [tex]\frac{2}{3} x[/tex] - 2
The slope is [tex]\frac{2}{3}[/tex]
Parallel lines are lines that never meets. Therefore they have the same slope;
the slope of the new line is [tex]\frac{2}{3}[/tex]
Now,
for the new line, we need to find the intercept;
since y = mx + c,
y = -4 and x = -6;
-4 = [tex]\frac{2}{3}[/tex] x (-6) + c
- 4 = -4 + c
c= 0
The equation of the new line is;
y = [tex]\frac{2}{3}[/tex]x
