What is the slope of a line perpendicular to the line whose equation is 12x+2y=-1212x+2y=−12. Fully reduce your answer.
1 answer:
Answer:
In this case the slope of a line perpendicular to the line whose equation is 12x+2y=-12 will be
Step-by-step explanation:
A line has the form:
y = m * x + b
where:
- m is the slope of the line.
- b is Y-intercept. This is the value of y where the line crosses the y-axis.
In this case, the line has the form 12*x+2*y=-12
First, you must isolate the variable "y", in order to arrive at the form of the line detailed above:
12*x+2*y=-12
2*y= -12 -12*x
y= (-12 -12*x)÷2
y= (-12)÷2 -(12÷2)*x
y= -6 -6*x
In this case: the slope is -6 and the Y-intercept is -6.
Two lines are perpendicular when they form four equal 90º angles. For two lines to be perpendicular, they must have their slopes inverse and changed sign.
Then, <u><em>in this case the slope of a line perpendicular to the line whose equation is 12x+2y=-12 will be </em></u><u><em /></u>
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We can set it up like this, where <em>s </em>is the speed of the canoeist:
To make a common denominator between the fractions, we can multiply the whole equation by s(s-5):
![s(s-5)[\frac{18}{s} + \frac{4}{s-5} = 3] \\ 18(s-5)+4s=3s(s-5) \\ 18s - 90+4s=3 s^{2} -15s](https://tex.z-dn.net/?f=s%28s-5%29%5B%5Cfrac%7B18%7D%7Bs%7D%20%2B%20%5Cfrac%7B4%7D%7Bs-5%7D%20%3D%203%5D%20%5C%5C%2018%28s-5%29%2B4s%3D3s%28s-5%29%20%5C%5C%2018s%20-%2090%2B4s%3D3%20s%5E%7B2%7D%20-15s)
If we rearrange this, we can turn it into a quadratic equation and factor:
Technically, either of these solutions would work when plugged into the original equation, but I would use the second solution because it's a little "neater." We have the speed for the first part of the trip (9 mph); now we just need to subtract 5mph to get the speed for the second part of the trip.
The canoeist's speed on the first part of the trip was 9mph, and their speed on the second part was 4mph.
To make a common denominator between the fractions, we can multiply the whole equation by s(s-5):
If we rearrange this, we can turn it into a quadratic equation and factor:
Technically, either of these solutions would work when plugged into the original equation, but I would use the second solution because it's a little "neater." We have the speed for the first part of the trip (9 mph); now we just need to subtract 5mph to get the speed for the second part of the trip.
The canoeist's speed on the first part of the trip was 9mph, and their speed on the second part was 4mph.