Answer:
[tex]y=\frac{3}{2}x-4[/tex]
Step-by-step explanation:
the equation of the line that passes through (4, 2) and is parallel to
3x – 2y = –6
Given equation of a line is [tex]3x-2y=-6[/tex]
Lets find the slope of the given line. Slope intercept form is
y=mx+b , where m is the slope
[tex]3x-2y=-6[/tex], subtract 3x on both sides
[tex]-2y=-3x-6[/tex]
Divide whole equation by -2
[tex]y=\frac{3}{2}x +2[/tex]
the slope of the given equation is [tex]\frac{3}{2}[/tex]
Slope of parallel line is same as the slope of the given line
the slope of the parallel line is [tex]\frac{3}{2}[/tex]
now we use point (4,2)
Use point slope form of a line
[tex]y=y1=m(x-x1)[/tex], where (x1,y1) is the given point and m is the slope
[tex]y-2=\frac{3}{2}(x-4)[/tex]
[tex]y-2=\frac{3}{2}x-6[/tex]
Add 2 on both sides
[tex]y=\frac{3}{2}x-4[/tex]
