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

5 km/h or 6 km/h

Step-by-step explanation:

Let the speed of the boat be xSpeed against the current in the river is x - 2

Time in the river:

6/(x - 2)

Time in the lake:

15/x

The difference:

6/(x - 2) = 15/x - 1

Solve for x to find the speed of the boat

Multiply both sides by x(x - 2) to clear the fraction:

6x = 15(x - 2) - x(x - 2)6x = 15x - 30 - x² + 2xx² - 11x + 30 = 0(x - 5)(x - 6) =0x -5 = 0, x - 6 = 0x = 5 km/h, x = 6 km/h