What is an equation of the line that passes through the point (6, -1) and is parallel to the line 2x-3y=12

y = -(2/3)x - 5

Step-by-step explanation:

First we need to find the slope of the line 2x - 3y = 12 by solving for y...

2x - 3y = 12

         -3y = -2x + 12

              y = (2/3)x - 4

Parallel lines have the same slope, so the new line has a slope of (2/3), the equation for a line is y = mx + b, so we have m, and a point (x, y) of (6, -1), so plug in all the values and solve for b...

-1 = (2/3)(6) + b

     -1 = 4 + b

             -5 = b

So the line parallel is y = (2/3)x - 5

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.