Answer:
What is the rule for a reflection across the line y =- X?
When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x).
Step-by-step explanation:
There is no rule about x=C..
Answer:
4x +y = 3
Step-by-step explanation:
Perpendicular lines have slopes that are the negative reciprocals of one another. When the equation of the line is written in standard form like this, the equation of the perpendicular line can be written by swapping the x- and y-coefficients and negating one of them. Doing this much would give you ...
4x +y = (constant)
Note that we have chosen to make the equation read 4x+y, not -4x-y. The reason is that "standard form" requires the leading coefficient to be positive.
Now, you just need to make sure the constant is appropriate for the point you want the line to go through. So, it needs to be ...
4(2) +(-5) = constant = 3
The line of interest has equation ...
4x + y = 3
12.5 gallons..............
For this case we have that by definition, the equation of a line of the point-slope form is given by:
![y-y_ {0} = m (x-x_ {0})](https://tex.z-dn.net/?f=y-y_%20%7B0%7D%20%3D%20m%20%28x-x_%20%7B0%7D%29)
Where:
m: It's the slope
It is a point through which the line passes
To find the slope, we need two points through which the line passes, observing the image we have:
![(x_ {1}, y_ {1}): (1,6)\\(x_ {2}, y_ {2}): (5, -2)\\m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-2-6} {5-1} = \frac {-8} {4} = -2](https://tex.z-dn.net/?f=%28x_%20%7B1%7D%2C%20y_%20%7B1%7D%29%3A%20%281%2C6%29%5C%5C%28x_%20%7B2%7D%2C%20y_%20%7B2%7D%29%3A%20%285%2C%20-2%29%5C%5Cm%20%3D%20%5Cfrac%20%7By_%20%7B2%7D%20-y_%20%7B1%7D%7D%20%7Bx_%20%7B2%7D%20-x_%20%7B1%7D%7D%20%3D%20%5Cfrac%20%7B-2-6%7D%20%7B5-1%7D%20%3D%20%5Cfrac%20%7B-8%7D%20%7B4%7D%20%3D%20-2)
Thus, the equation is of the form:
![y-y_ {0} = - 2 (x-x_ {0})](https://tex.z-dn.net/?f=y-y_%20%7B0%7D%20%3D%20-%202%20%28x-x_%20%7B0%7D%29)
We choose a point:
![(x_{0}, y_ {0}) :( 5, -2)](https://tex.z-dn.net/?f=%28x_%7B0%7D%2C%20y_%20%7B0%7D%29%20%3A%28%205%2C%20-2%29)
Finally, the equation is:
![y - (- 2) = - 2 (x-5)\\y + 2 = -2 (x-5)](https://tex.z-dn.net/?f=y%20-%20%28-%202%29%20%3D%20-%202%20%28x-5%29%5C%5Cy%20%2B%202%20%3D%20-2%20%28x-5%29)
Answer:
![y + 2 = -2 (x-5)](https://tex.z-dn.net/?f=y%20%2B%202%20%3D%20-2%20%28x-5%29)
The answer is C because it fits the formula a+b=c
2+4=6