3X + 12 = 36
1 answer:
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[1] The median to the base passes through the top point (0,b) and the bottom point (0,0) since it is going straight down. The slope formula is
So, the slope of the median is (b-0)/(0-0) = b/0. Technically, this is undefined, but let's leave it this way for now.
[2] The base passes through the left point (-a,0) and the right point (a,0). Its slope must be (0-0)/(a-(-a)) = 0.
[3] We now check if the slopes are negative reciprocals. Flipping b/0 over and putting a negative sign gives:
b/0 -> - 0/b = 0
So the slopes are negative reciprocals, which means the lines are perpendicular.
So, the slope of the median is (b-0)/(0-0) = b/0. Technically, this is undefined, but let's leave it this way for now.
[2] The base passes through the left point (-a,0) and the right point (a,0). Its slope must be (0-0)/(a-(-a)) = 0.
[3] We now check if the slopes are negative reciprocals. Flipping b/0 over and putting a negative sign gives:
b/0 -> - 0/b = 0
So the slopes are negative reciprocals, which means the lines are perpendicular.
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.