⚠️15 points⚠️
2 answers:
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Answer:
15 = 2x - 3y
Step-by-step explanation:
We have the two points P1(3,-3) and P2(9,1).
First, calculate the slope between those points:
slope
Now simply move 3 steps from (3,-3) towards the y-axis to get the intersection with the y-axis (each step reduces x by 1 and applies the slope to the y-value):
(3,-3)
---> (2, -3 - (2/3)) = (2,-3 2/3)
---> (1, (-3 2/3) - 2/3) = (1, -4 1/3)
---> (0, (-4 1/3) - 2/3) = (0,-5)
This tells us, that our line intersects the y-axis at (0,-5).
The general form of a line is f(x) = <SLOPE> * x + <Y-VALUEATXEQUALSZERO>.
In our case: f(x) = y = (2/3)x -5.
To get it into the correct form, we simply subtract y from both sides and get:
0 = (2/3)x - y - 5
To get only integers just multiply everything with 3 and add 15 and get:
15 = 2x - 3y, which fulfils the form asked for in the problem.
If we let x and y represent length and width, respectively, then we can write equations according to the problem statement.
.. x = y +2
.. xy = 3(2(x +y)) -1
This can be solved a variety of ways. I find a graphing calculator provides an easy solution: (x, y) = (13, 11).
The length of the rectangle is 13 inches.
The width of the rectangle is 11 inches.
______
Just so you're aware, the problem statement is nonsensical. You cannot compare perimeter (inches) to area (square inches). You can compare their numerical values, but the units are different, so there is no direct comparison.
.. x = y +2
.. xy = 3(2(x +y)) -1
This can be solved a variety of ways. I find a graphing calculator provides an easy solution: (x, y) = (13, 11).
The length of the rectangle is 13 inches.
The width of the rectangle is 11 inches.
______
Just so you're aware, the problem statement is nonsensical. You cannot compare perimeter (inches) to area (square inches). You can compare their numerical values, but the units are different, so there is no direct comparison.