Question

What is the equation of the line that passes through (4, 2) and is parallel to 3x – 2y = –6?

Answer 1

The question is asking to choose among the following choices that states the equation of the line that passes through (4,2) and is parallel to 3x-2y=-6, base on my calculation and further analysis, I would say that the answer would be y=-3/2x+8. I hope you are satisfied with my answer and feel free to ask for more 

Answer 2

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

$y=\frac{3}{2}x-4$