Respuesta :

yonasdg24

Answer:

Step-by-step explanation:

If it is parallel with the line 2x-3y=9

Both of them have same slope so

2x-3y=9 turn this into slope intercept form first

-3y=9-2x

Y=9/-3 + -2x/-3

Y=2/3x - 3 the slope of this equation is ⅔

So our new equation will be

Y=⅔x +b

Since (6,7)

On the line

6=⅔(7)+b

b= 6-14/3=4/3

Y=⅔x+4/3 (slope intercept form)

3y-2x=4 ( general equation of line )

abidemiokin

The equation of the line that passes through the point (6, 7) and is parallel to the line 2x - 3y = 9 is 3y -2x = 19

The equation of a line in point slope form is expressed as

y-y0 = m(x-x0)

m is the slope of the line

(x0, y0) is the point on the line.

Given the equation 2x - 3y = 9

Rewrite in standard form y = mx + b

-3y = -2x + 9

y = 2/3 x - 3

Compared with the standard, the slope of the line is 2/3

Substitute the slope and the point into the point slope equation.

y - 7 = 2/3 (x - 6)

3(y-7) = 2(x-6)

3y - 21 = 2x - 2

3y - 2x = 19

Hence the equation of the line that passes through the point (6, 7) and is parallel to the line 2x - 3y = 9 is 3y -2x = 19

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