Part A)
Given
Using the point-slope form of the line equation

where
m is the slope of the line
(x₁, y₁) is the point
In our case:
substituting the values m = 6 and the point (x₁, y₁) = (7, 2) in the point-slope form of the line equation


Therefore, the equation in point-slope form for the line having the slope m = 6 and containing the points (7,2) will be:

Part B)
Given
Using the point-slope form of the line equation

where
m is the slope of the line
(x₁, y₁) is the point
In our case:
substituting the values m = -3 and the point (x₁, y₁) = (3, 8) in the point-slope form of the line equation


Therefore, the equation in point-slope form for the line having the slope m = -3 and containing the points (3, 8) will be:
Write a system of equations:
x + y = 125
20x + 15y = 2100
Solving:
x = 125 - y
20(125 - y) + 15y = 2100
2500 - 20y + 15y = 2100
2500 - 5y = 2100
-5y = 2100 - 2500
-5y = -400
y=80
x + 80 = 125
x = 125 - 80
x = 45
The first charges 45$ per hour and the second charges 80$ per hour
Answer:
a. the ratio of the sides is 6: 8, or 3:4
b. the ratio of the surfaces is
or 9:16, the square of the ratio of the sides.
c. the ratio of the volumes is
or 27:64, the cube of the ratio of the sides.
Divide how many roses they use by how many is in each: 882/3=294. They sell 294 vases :)