Answer:
[tex]y = - \frac{ 3}{2} x[/tex]
Step-by-step explanation:
slope-intercept form
y= mx +c, where m is the slope and c is the y-intercept.
Let's rewrite the given equation into the slope-intercept form so we can find out its gradient.
3x +2y -6= 0
2y= -3x +6
Dividing by 2 throughout:
[tex]y = - \frac{3}{2} x + 3[/tex]
Thus gradient of given line= [tex] - \frac{3}{2} [/tex]
Parallel lines have the same gradient.
Thus gradient of line= [tex] - \frac{3}{2} [/tex]
Subst. m=[tex] - \frac{3}{2} [/tex] into the equation:
[tex]y = - \frac{3}{2}x + c[/tex]
To find c, substitute a pair of coordinates.
When x=0, y=0,
[tex]0 = - \frac{3}{2} (0) + c \\ c = 0[/tex]
Thus, the equation of the line is [tex]y = - \frac{3}{2} x[/tex].
