To construct the equations for these lines, we are going to use the point-slope formula, which is:
![(y - y_1) = m(x - x_1)](https://tex.z-dn.net/?f=%28y%20-%20y_1%29%20%3D%20m%28x%20-%20x_1%29)
is the slope of the line
is a point on the line
1)
In this case, our point is (2, -1) and our line has a slope of 5. (Remember that the line is parallel, meaning that it has the same slope as the given line. Since the line is in the y = mx + b format, we could easily pick out the slope m as being 5.)
Thus, we can "plug in" what we know into our formula to find the equation of our line:
![(y + 1) = 5(x - 2)](https://tex.z-dn.net/?f=%28y%20%2B%201%29%20%3D%205%28x%20-%202%29)
![(y + 1) = 5x - 10](https://tex.z-dn.net/?f=%28y%20%2B%201%29%20%3D%205x%20-%2010)
![y = 5x - 11](https://tex.z-dn.net/?f=y%20%3D%205x%20-%2011)
2)
We are going to do the same thing, except our point is now (0, -5) and our slope is now 9.
![(y + 5) = 9(x - 0)](https://tex.z-dn.net/?f=%28y%20%2B%205%29%20%3D%209%28x%20-%200%29)
![y = 9x - 5](https://tex.z-dn.net/?f=y%20%3D%209x%20-%205)
Our equations are:
1) y = 5x - 11
2) y = 9x - 5
Answer:
14 and 12
Step-by-step explanation:
Answer:
Step-by-step explanation:
The range of a function is the set of all possible values it can produce.
For example, consider the function
![f(x)=x^{2}](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E%7B2%7D)
No matter what value we give to x, the function is always positive:
If x is 2, then the function returns x squared or 4.
If x is negative 2, then it still produces 4 since -2 times -2 is positive 4.
So the range of the function is
"all real numbers greater than or equal to zero".
For this case we must find the value of "x" of the following equation:
![x ^ 2-9 = 0](https://tex.z-dn.net/?f=x%20%5E%202-9%20%3D%200)
So:
We add 9 to both sides of the equation:
![x ^ 2-9 + 9 = 9\\x ^ 2 = 9](https://tex.z-dn.net/?f=x%20%5E%202-9%20%2B%209%20%3D%209%5C%5Cx%20%5E%202%20%3D%209)
We apply square root on both sides of the equation to eliminate the exponent on the left side:
![x = \pm \sqrt {9}](https://tex.z-dn.net/?f=x%20%3D%20%5Cpm%20%5Csqrt%20%7B9%7D)
Thus, the solutions are:
![x_ {1} = + 3\\x_ {2} = - 3](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%20%2B%203%5C%5Cx_%20%7B2%7D%20%3D%20-%203)
ANswer:
![x_ {1} = + 3\\x_ {2} = - 3](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%20%2B%203%5C%5Cx_%20%7B2%7D%20%3D%20-%203)
Opcion C