Question:
Find the constant of proportionality k. Then write an equation for the relationship between x and y
![\begin{array}{ccccc}x & {2} & {4} & {6} & {8} \ \\ y & {10} & {20} & {30} & {40} \ \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccccc%7Dx%20%26%20%7B2%7D%20%26%20%7B4%7D%20%26%20%7B6%7D%20%26%20%7B8%7D%20%5C%20%5C%5C%20y%20%26%20%7B10%7D%20%26%20%7B20%7D%20%26%20%7B30%7D%20%26%20%7B40%7D%20%5C%20%5C%20%5Cend%7Barray%7D)
Answer:
(a) ![k = 5](https://tex.z-dn.net/?f=k%20%3D%205)
(b) ![y = 5x](https://tex.z-dn.net/?f=y%20%3D%205x)
Step-by-step explanation:
Given
![\begin{array}{ccccc}x & {2} & {4} & {6} & {8} \ \\ y & {10} & {20} & {30} & {40} \ \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccccc%7Dx%20%26%20%7B2%7D%20%26%20%7B4%7D%20%26%20%7B6%7D%20%26%20%7B8%7D%20%5C%20%5C%5C%20y%20%26%20%7B10%7D%20%26%20%7B20%7D%20%26%20%7B30%7D%20%26%20%7B40%7D%20%5C%20%5C%20%5Cend%7Barray%7D)
Solving (a): The constant of proportionality:
Pick any two corresponding x and y values
![(x_1,y_1) = (2,10)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%282%2C10%29)
![(x_2,y_2) = (6,30)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%286%2C30%29)
The constant of proportionality k is:
![k = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
![k = \frac{30-10}{6-2}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B30-10%7D%7B6-2%7D)
![k = \frac{20}{4}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B20%7D%7B4%7D)
![k = 5](https://tex.z-dn.net/?f=k%20%3D%205)
Solving (b): The equation
In (a), we have:
![(x_1,y_1) = (2,10)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%282%2C10%29)
k can also be expressed as:
![k = \frac{y- y_1}{x- x_1}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7By-%20y_1%7D%7Bx-%20x_1%7D)
Substitute values for x1, y1 and k
![5 = \frac{y- 10}{x- 2}](https://tex.z-dn.net/?f=5%20%3D%20%5Cfrac%7By-%2010%7D%7Bx-%202%7D)
Cross multiply:
![y - 10 = 5(x - 2)](https://tex.z-dn.net/?f=y%20-%2010%20%3D%205%28x%20-%202%29)
Open bracket
![y - 10 = 5x - 10](https://tex.z-dn.net/?f=y%20-%2010%20%3D%205x%20-%2010)
Add 10 to both sides
![y - 10 +10= 5x - 10+10](https://tex.z-dn.net/?f=y%20-%2010%20%2B10%3D%205x%20-%2010%2B10)
![y = 5x](https://tex.z-dn.net/?f=y%20%3D%205x)
Card A:
<span>$4,350 x 0.02 = $87
</span><span>$360 - $87 = $273
Card B:
Interest $270 no rebate
so $273 - $270 = $3
Card B cost least and $3 less than card A</span>
Answer:
7/15 is greater than 5/11
Step-by-step explanation:
7/15= .4667
5/11= .454545
Hope that's helpful
i’m pretty positive you would just subtract!
Answer:
3333.6
Step-by-step explanation:
bc i said soo