Question
In the xy-plane, the point (p, r) lies on the line with equation y = x + b, where b is a constant. The point with coordinates (2p, 5r) lies on the line with equation y = 2x + b. If p ≠ 0, what is the value of 
?
The correct answer is:
If point (p, r), lie on the line with equation y = x + b,
y = r, and x = p
r = p + b
b = r - p ---------- eqn(1)
Also, (2p, 5r) lies on the line with equation y = 2x + b
x = 2p, and y = 5r
5r = 2(2p) + b
5r = 4p + b
b = 5r - 4p -------- eqn(2)
Since eqn(1) and eqn(2) are on the same line, their intercept are the same. That is eqn(1) = eqn(2)
r - p = 5r - 4p
- p + 4p = 5r - r
3p = 4r
Thus, r/p = 3/4
If we have coordinates of two points on a line, then we can use the slope formula to determine that line's slope. m = (y2-y1) / (x2-x1), or the ratio of the change in the y values and the x values, is the slope formula. 'x1' and 'y1' are the coordinates of the first point. The second points have the coordinates x2 and y2. If you have two points, you can always calculate the slope of a line. If you don't have access to two points, you can locate two points on the graph and use those to calculate the slope.
¶Observe the following helpful information:
- m = slope
¶-Rise = the difference between the y-values (y2 - y1), where (x1, y1) = point 1 and (x2, y2) = point 2.
Run is equal to the difference between x-values (x2 - x1).
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A fashion buyer for a large retail store purchased 315 items directly from the manufacturer for a total of $6000. Some of the items were dresses purchased for $25 each, and the rest were shirts purchased for $10 each. How many more dresses than shirts did the buyer purchase?
A purchase price is the economic value, usually expressed in fiat currency at the time of purchase, for which a buyer pays for a product, service, or asset. The compensation for this value can be in the form of fiat currency or something else, such as services as payment or benefits in kind.
A purchase formula is a formula that is used to calculate the invoice amount, including discounts and taxes. The default Purchase formula is not always useful to users because the invoice amount calculation varies for different suppliers depending on the type of origin of the arrived goods, tax, and other charges levied on the purchased items.
The basic amount is the gross amount. It is the sum that includes only the purchase price of the items.
Gross Amount = Quantity * Purchase Price
1, what is the value of 
?
