Give the equation of the line goinng through (4, 6) and parallel to the line 2y-6x=4

y = 3x-6

Step-by-step explanation:

First we need to find the slope of the line

2y-6x=4

Solve for y

Add 6x to each side

2y-6x+6x=4+6x

2y = 6x+4

Divide each side by 2

2y/2 =6x/2 +4/2

y = 3x +2

The slope is 3

We want a line parallel, so it will have the same slope

We have a slope and a point

y = 3m+b

Substitute in the point

6 = 3(4)+b

6 =12+b

Subtract 12 from each side

6-12 = 12-12+b

-6 =b

y = 3x-6

y = 3x - 6

Step-by-step explanation:

2y = 6x + 4

y = 3x + 2

Slope = 3

y = 3x + c

6 = 3(4) + c

c = 6 - 12

c = -6

y = 3x - 6

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: