There follows the formula for "z-score:"
raw score - mean
z = ------------------------------
standard dev
9.1 - 8
Here, the z-score is z = ------------- = 0.344
3.2
We have to determine the equation of the line passing through the point (2,-5) and parallel to the line ![5x = 6y+7](https://tex.z-dn.net/?f=5x%20%3D%206y%2B7)
When two lines are parallel, then the slopes of the two lines are equal.
Equation of line with point
and slope 'm' is given by:
![(y-y_1) = m(x-x_1)](https://tex.z-dn.net/?f=%28y-y_1%29%20%3D%20m%28x-x_1%29)
Since, we have to determine the equation of a line with point (2,-5).
So, the equation of the line is : ![(y-(-5)) = m(x-2)](https://tex.z-dn.net/?f=%28y-%28-5%29%29%20%3D%20m%28x-2%29)
![y+5 = m(x-2)](https://tex.z-dn.net/?f=y%2B5%20%3D%20m%28x-2%29)
Since, the line is parallel to the line ![5x = 6y+ 7](https://tex.z-dn.net/?f=5x%20%3D%206y%2B%207)
So, ![6y +7 = 5x](https://tex.z-dn.net/?f=6y%20%2B7%20%3D%205x)
![6y = 5x - 7](https://tex.z-dn.net/?f=6y%20%3D%205x%20-%207)
![y = \frac{5}{6}x - \frac{7}{6}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B5%7D%7B6%7Dx%20-%20%5Cfrac%7B7%7D%7B6%7D)
So, slope of the line 'm' is
.
Therefore, the equation of the line is:
![(y+5) = \frac{5}{6}(x-2)](https://tex.z-dn.net/?f=%28y%2B5%29%20%3D%20%5Cfrac%7B5%7D%7B6%7D%28x-2%29)
![6y + 30 = 5x - 10](https://tex.z-dn.net/?f=6y%20%2B%2030%20%3D%205x%20-%2010)
![6y - 5x = -10-30](https://tex.z-dn.net/?f=6y%20-%205x%20%3D%20-10-30)
![6y - 5x = -40](https://tex.z-dn.net/?f=6y%20-%205x%20%3D%20-40)
Therefore,
is the required equation of the line.
First step is square root both sides leaving with
x-6=+/-3
closest one is A
answer is A
Let julia's age be x
Let Kara's age be 4x
x+4x=13
5x=13
x=13/5
2.6 years
-Move 2 units left:y=(1/x +2)
-Move 3 units up:y= (1/x +2)+3
So the equation is y= (1/x +2)+3