Answer:
![y=\displaystyle\frac{3}{4} x+\displaystyle \frac{1}{4}](https://tex.z-dn.net/?f=y%3D%5Cdisplaystyle%5Cfrac%7B3%7D%7B4%7D%20x%2B%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B4%7D)
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form:
where <em>m</em> is the slope and <em>b</em> is the y-intercept (the value of y when x=0).
First, we must find the slope (<em>m</em>).
where two points that fall on the line are
and ![(x_2,y_2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29)
Two points that are highlighted for us on the graph are (-3,-2) and (5,4). Plug these into the equation:
![m=\displaystyle\frac{4-(-2)}{5-(-3)}\\\\m=\displaystyle\frac{4+2}{5+3}\\\\m=\displaystyle\frac{6}{8}\\\\m=\frac{3}{4}](https://tex.z-dn.net/?f=m%3D%5Cdisplaystyle%5Cfrac%7B4-%28-2%29%7D%7B5-%28-3%29%7D%5C%5C%5C%5Cm%3D%5Cdisplaystyle%5Cfrac%7B4%2B2%7D%7B5%2B3%7D%5C%5C%5C%5Cm%3D%5Cdisplaystyle%5Cfrac%7B6%7D%7B8%7D%5C%5C%5C%5Cm%3D%5Cfrac%7B3%7D%7B4%7D)
Therefore, the slope of the line is 3/4. Plug this into
:
![y=\displaystyle\frac{3}{4} x+b](https://tex.z-dn.net/?f=y%3D%5Cdisplaystyle%5Cfrac%7B3%7D%7B4%7D%20x%2Bb)
Now, to find the y-intercept (<em>b</em>), our first resort would be to find it on the graph. However, on the graph, it appears ambiguous. So, we must solve it algebraically.
![y=\displaystyle\frac{3}{4} x+b](https://tex.z-dn.net/?f=y%3D%5Cdisplaystyle%5Cfrac%7B3%7D%7B4%7D%20x%2Bb)
Plug in the point (5,4) and solve for <em>b</em>:
![4=\displaystyle\frac{3}{4} (5)+b\\\\4=\displaystyle\frac{15}{4}+b\\\\b=4-\frac{15}{4} \\\\b=\frac{1}{4}](https://tex.z-dn.net/?f=4%3D%5Cdisplaystyle%5Cfrac%7B3%7D%7B4%7D%20%285%29%2Bb%5C%5C%5C%5C4%3D%5Cdisplaystyle%5Cfrac%7B15%7D%7B4%7D%2Bb%5C%5C%5C%5Cb%3D4-%5Cfrac%7B15%7D%7B4%7D%20%5C%5C%5C%5Cb%3D%5Cfrac%7B1%7D%7B4%7D)
Therefore, the y-intercept is
. Plug this back into
:
![y=\displaystyle\frac{3}{4} x+\displaystyle \frac{1}{4}](https://tex.z-dn.net/?f=y%3D%5Cdisplaystyle%5Cfrac%7B3%7D%7B4%7D%20x%2B%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B4%7D)
I hope this helps!
Answer: r = I/pt
Step-by-step explanation:
Interest divided by the principal × time gives the rate. It's usually expressed as a percentage per year.
Answer:
80%
Step-by-step explanation:
it’s 82% but rounded its 80
Answer:
There will be 20 914 rupees in the amount at the end of 3 years.
Step-by-step explanation:
The amount of rupes after t years in compound interest is given by:
![A(t) = A(0)(1+r)^{t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%281%2Br%29%5E%7Bt%7D)
In which A(0) is the initial amount and r is the interest rate, as a decimal.
Hiran invests 20 000 rupees in an account for 3 years at 1.5% per year compound interest.
This means that
. So
![A(t) = A(0)(1+r)^{t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%281%2Br%29%5E%7Bt%7D)
![A(t) = 20000(1+0.015)^{t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%2020000%281%2B0.015%29%5E%7Bt%7D)
![A(t) = 20000(1.015)^{t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%2020000%281.015%29%5E%7Bt%7D)
Work out the total amount of money in the account at the end of 3 years.
This is A(3). So
![A(3) = 20000(1.015)^{3} = 20913.6](https://tex.z-dn.net/?f=A%283%29%20%3D%2020000%281.015%29%5E%7B3%7D%20%3D%2020913.6)
Rounding to the nearest rupee.
There will be 20 914 rupees in the amount at the end of 3 years.