The equation of line is: [tex]y=-\frac{3}{2}x[/tex] as the y-intercept is zero
Step-by-step explanation:
Given
(-2,3)
Equation of line => 3x+2y=6
Converting the equation in slope intercept form
[tex]3x+2y=6\\2y=-3x+6\\Dividing\ both\ sides\ by\ 2\\\frac{2y}{2}=-\frac{3}{2}x+\frac{6}{2}\\y=-\frac{3}{2}x+3[/tex]
The co-efiicient of x is the slope of the fiven line
So,
m=-3/2
The line parallel to given line will have the same slope as slopes of two parallel lines are equal
Now,
Slope-intercept form is:
[tex]y=mx+b[/tex]
Putting the value of slope
[tex]y=-\frac{3}{2}x+b[/tex]
to find the value of b, put (-2,3) in the equation
[tex]3=-\frac{3}{2}(-2)+b\\3=3+b\\b=0\\[/tex]
Putting the value of b and m
[tex]y=-\frac{3}{2}x+0\\y=-\frac{3}{2}x[/tex]
Hence,
The equation of line is: [tex]y=-\frac{3}{2}x[/tex] as the y-intercept is zero
Keywords: Slope-intercept form, Slope
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