In all of these cases, y=x+2.
A parallelogram should have 2 sets of parallel lines. Let's find the slope of line PQ and RS to test.
PQ:
(4-2)/(1-(-3))
2/4
1/2
RS:
(2-0)/(3-1)
2/2
1
Because 1 does not equal 1/2 (the slopes are different) the lines are not parallel. Thus, the figure is not a parallelogram.
Robbie bought the smallest amount. Let's use x for that amount.
Let's use n for amount that each following customer increases.
We have:
Robbie=x
Cameron=x+n
Louis=x+n+n
Tom=x+n+n+n
Charlie=x+n+n+n+n
We know that they bought total of 60 scones.
Robbie + Cameron + Louis + Tom + Charlie = 60
x + x+n + x+n+n + x+n+n+n + x+n+n+n+n = 60
5x + 10n = 60 /:5
x + 2n = 12
We are also given this information:
(Robbie + Cameron) = 3/7 * (Louis + Tom + Charlie)
We insert the equations from above:
(x + x+n) = 3/7 * (x+n+n + x+n+n+n + x+n+n+n+n)
2x + n = 3/7 * (3x + 9n) /*7
14x + 7n = 3* (3x + 9n)
14x +7n = 9x + 27n
We take everything on the left side.
14x + 7n - 9x - 27n = 0
5x - 20n = 0/:5
x - 4n = 0
Now we have two equations:
x + 2n = 12
x - 4n = 0
We solve second one for x and insert it into first one.
x + 2n = 12
x = 4n
4n + 2n =12
6n = 12 /:6
n = 2
x=4*2
x=8
Now we can solve for the amount for each customer.
Robbie=x = 8
Cameron=x+n = 8 + 2 = 10
Louis=x+n+n = 8 + 2 + 2 = 12
Tom=x+n+n+n = 8 + 2 + 2 + 2 = 14
Charlie=x+n+n+n+n = 8 + 2 + 2 + 2 + 2 = 16
3.
30 divided by 10 equals 3
The slope of the line is the velocity, or rate of change, of y with respect to x. In other terms, the slope tells you how much y will change for every change in x by one unit. For example if the slope, which is velocity, is 2. y will increase by two units every time x increases by one unit. Your graph is not pictured nor explained, so I cannot give you the specific context beyond the principle that the slope of a line is a constant velocity or rate of change.
