First of all, let's find the slope of line L. To find the slope of a line, you write it in the explitic form
, and consider the coefficient
. So, we have
![2x - 3y = 5 \iff 3y = 2x-5 \iff y = \dfrac{2}{3} x - \dfrac{5}{3}](https://tex.z-dn.net/?f=%202x%20-%203y%20%3D%205%20%5Ciff%203y%20%3D%202x-5%20%5Ciff%20y%20%3D%20%5Cdfrac%7B2%7D%7B3%7D%20x%20-%20%5Cdfrac%7B5%7D%7B3%7D%20)
So, the slope of line L is 2/3.
Two lines are parallel if they have the same slope. So, line M has slope 2/3 as well, and we know that it passes through the point (3, -10).
When you are given the slope
and a point
of a line, its equation is given by
![y-y_0=m(x-x_0)](https://tex.z-dn.net/?f=%20y-y_0%3Dm%28x-x_0%29%20)
So, if you plug your values, you have
![y+10 = \dfrac{2}{3}(x-3)](https://tex.z-dn.net/?f=%20y%2B10%20%3D%20%5Cdfrac%7B2%7D%7B3%7D%28x-3%29%20)
which you can simplify into
![y+10 = \dfrac{2}{3}x-2](https://tex.z-dn.net/?f=%20y%2B10%20%3D%20%5Cdfrac%7B2%7D%7B3%7Dx-2%20)
![y = \dfrac{2}{3}x-12](https://tex.z-dn.net/?f=%20y%20%3D%20%5Cdfrac%7B2%7D%7B3%7Dx-12%20)
Y=mx+b
14=1(-4)+18
This could be an example of an equation in slope intersect form, where y=14 and x=-4
Answer:
What are the options???????
Step-by-step explanation:
Answer:
1,269 students
Step-by-step explanation:
Z-score for a 90% confidence interval (z) = 1.645
The proportion of students who own their own car (p) = 0.25
Standard error = 0.02
The standard error of a proportion is given by:
![SE = z*\sqrt{\frac{p*(1-p)}{n} }](https://tex.z-dn.net/?f=SE%20%3D%20z%2A%5Csqrt%7B%5Cfrac%7Bp%2A%281-p%29%7D%7Bn%7D%20%7D)
Applying the given values, the sample size 'n' needed is:
![0.02 = 1.645*\sqrt{\frac{0.25*(1-0.25)}{n} }\\n=0.25*0.75*(\frac{1.645}{0.02})^2 \\n=1,268.45\ students](https://tex.z-dn.net/?f=0.02%20%3D%201.645%2A%5Csqrt%7B%5Cfrac%7B0.25%2A%281-0.25%29%7D%7Bn%7D%20%7D%5C%5Cn%3D0.25%2A0.75%2A%28%5Cfrac%7B1.645%7D%7B0.02%7D%29%5E2%20%5C%5Cn%3D1%2C268.45%5C%20students)
Rounding up to the next whole student, the sample size needed is 1,269 students.