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