What is the equation of the line perpendicular to 2x - 3y = 13 that passes through the point (-6, 5)?

2y + 3x = -8.

Step-by-step explanation:

Given our first equation 2x-3y =13, we rewrite in the form of equation of a line, i.e y = mx + c

Where m is the slope of the line and c is the intersection on y axis.

By rewriting, we have...

3y= 2x-13

y= 2x/3 - 13/3.

m= 2/3, c= -13/3.

For two perpendicular lines, the product of their gradients is -1

i.e

m¹ * m² = -1

Hence m² = -1 * 3/2

m² = -3/2.

Hence, to get the equation of the line passing through the point (-6,5) we first find the intersection when x=0 given as

[Y-c]/[x-0] = -3/2

2y - 2c = -3x

2(5) - 2c =- 3(-6)

10-18= 2c

C = -8/2

C= -4

Then the equation is given as

y = mx + c

y = [-3/2]x - 4

2y= -3x - 8

2y + 3x = -8.

$18 was the price of the t-shirt

step-by-step explanation:

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.