Question

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

Answer 1

3x-2y=-6
2y = 3x + 6
y = 3/2x + 3 so slope = 3/2
parallel lines have same slope, also has slope = 3/2

passes through (4,2) 
y = mx + b
2 = 3/2(4) + b
2 = 6 + b
b = -4

equation
y = 3/2x - 4

standard form
3x - 2y = 8

Answer 2

Hi! ❄

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Hi there, you first need to subtract by 3x both sides.

$\sf{-2y=6-3x}$

You can re-arrange the order of the last two terms,

$\sf{-2y=-3x+6}$

And Now, divide the entire equation by -2.

$\sf{y=\dfrac{-3}{-2}x-3}$

$\sf{y=\dfrac{3}{2}x-3}$

Keeping in mind that parallel lines have equal slopes,

we can find the equation of the second line.

Slope = $\it{\dfrac{3}{2}x}$

Point intercepted by the line = (4,2)                       $\large{\begin{gathered} \sf{Multiplying \ fractions} \\ \dfrac{3}{2}\times-\frac{4}{1} =-\frac{12}{2}=-6 \end{gathered}}$

Using Point-slope formula,

$\sf{y-y_1=m(x-x_1)}$

put in the pieces of information we know

$\sf{y-2=\dfrac{3}{2}(x-4)}$

Now distribute 3/2

$\sf{y-2=\dfrac{3}{2}x-^-6}$

$\sf{y-2=\dfrac{3}{2}x+6}$

Add by 2 both sides

$\sf{y=\dfrac{3}{2}x+8}$

Hope that made sense !!

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