Given:
The graph of linear function.
To find:
The slope intercept form of the linear equation from the given graph.
Solution:
The slope intercept form of a linear function is:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
From the given graph it is clear that the graph passes through the points (1,300) and (4,800).
The equation of line is
![y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29)
![y-300=\dfrac{800-300}{4-1}(x-1)](https://tex.z-dn.net/?f=y-300%3D%5Cdfrac%7B800-300%7D%7B4-1%7D%28x-1%29)
![y-300=\dfrac{500}{3}(x-1)](https://tex.z-dn.net/?f=y-300%3D%5Cdfrac%7B500%7D%7B3%7D%28x-1%29)
![y-300=\dfrac{500}{3}x-\dfrac{500}{3}](https://tex.z-dn.net/?f=y-300%3D%5Cdfrac%7B500%7D%7B3%7Dx-%5Cdfrac%7B500%7D%7B3%7D)
Adding 300 on both sides, we get
![y=\dfrac{500}{3}x-\dfrac{500}{3}+300](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B500%7D%7B3%7Dx-%5Cdfrac%7B500%7D%7B3%7D%2B300)
![y=\dfrac{500}{3}x+\dfrac{900-500}{3}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B500%7D%7B3%7Dx%2B%5Cdfrac%7B900-500%7D%7B3%7D)
![y=\dfrac{500}{3}x+\dfrac{400}{3}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B500%7D%7B3%7Dx%2B%5Cdfrac%7B400%7D%7B3%7D)
Therefore, the required equation is
.
the answer to the equation is -9
K=5, I found this by dividing 0.7 by 0.14. Then just substitute 5 in for K in the formula.
Answer:
(1) The annual interest rate is 10%, that is greater than 8%
(2) The annual interest is bigger than 22.47% and that is greater than 8%
Step-by-step explanation:
We have the equation:
![I=1,000((1+\frac{r}{100} )^{n} -1)](https://tex.z-dn.net/?f=I%3D1%2C000%28%281%2B%5Cfrac%7Br%7D%7B100%7D%20%29%5E%7Bn%7D%20-1%29)
Where I is the earns in interest, n is the number of years and r is the annual interest rate.
For the first case, we can replace I by $210 and n by 2 as:
![210=1,000((1+\frac{r}{100} )^{2} -1)](https://tex.z-dn.net/?f=210%3D1%2C000%28%281%2B%5Cfrac%7Br%7D%7B100%7D%20%29%5E%7B2%7D%20-1%29)
Solving for r, we get:
![\frac{210}{1,000} = (1+\frac{r}{100})^{2} -1](https://tex.z-dn.net/?f=%5Cfrac%7B210%7D%7B1%2C000%7D%20%3D%20%281%2B%5Cfrac%7Br%7D%7B100%7D%29%5E%7B2%7D%20-1)
![0.21 +1 = (1+\frac{r}{100})^{2}](https://tex.z-dn.net/?f=0.21%20%2B1%20%3D%20%281%2B%5Cfrac%7Br%7D%7B100%7D%29%5E%7B2%7D)
![1.21 = (1+\frac{r}{100})^{2}](https://tex.z-dn.net/?f=1.21%20%3D%20%281%2B%5Cfrac%7Br%7D%7B100%7D%29%5E%7B2%7D)
![\sqrt{1.21} = 1 + \frac{r}{100}](https://tex.z-dn.net/?f=%5Csqrt%7B1.21%7D%20%3D%201%20%2B%20%5Cfrac%7Br%7D%7B100%7D)
![\sqrt{1.21} - 1 = \frac{r}{100}](https://tex.z-dn.net/?f=%5Csqrt%7B1.21%7D%20-%201%20%3D%20%5Cfrac%7Br%7D%7B100%7D)
![(\sqrt{1.21} - 1)100=r](https://tex.z-dn.net/?f=%28%5Csqrt%7B1.21%7D%20-%201%29100%3Dr)
![10=r](https://tex.z-dn.net/?f=10%3Dr)
So, for the first case, the interest rate paid by the bank is 10% and it is greater than 8%
For the second case, we need to take the equation and solve for r as:
![(1+\frac{r}{100} )^{2} >1.5](https://tex.z-dn.net/?f=%281%2B%5Cfrac%7Br%7D%7B100%7D%20%29%5E%7B2%7D%20%3E1.5)
![1+\frac{r}{100} > \sqrt{1.5}](https://tex.z-dn.net/?f=1%2B%5Cfrac%7Br%7D%7B100%7D%20%3E%20%5Csqrt%7B1.5%7D)
![\frac{r}{100} > \sqrt{1.5}-1](https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7B100%7D%20%3E%20%5Csqrt%7B1.5%7D-1)
![r > (\sqrt{1.5}-1)*100](https://tex.z-dn.net/?f=r%20%3E%20%28%5Csqrt%7B1.5%7D-1%29%2A100)
![r > 22.47](https://tex.z-dn.net/?f=r%20%3E%2022.47)
So, for the second case the rate need to be bigger than 22.47% and that is bigger than 8%
Answer:
It is still sideways
Step-by-step explanation: