Answer:
y = 8x+8
Step-by-step explanation:
We can solve for the function by finding the slope of the linear function using two points. Let's use (0,8) and (1,16)
Slope formula is: ![m = \frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By2-y1%7D%7Bx2-x1%7D)
Plug in the 2 points: ![m = \frac{16-8}{1-0}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B16-8%7D%7B1-0%7D)
Simplify: m = 8
So now, for the equation y = mx+b, we have m which is y = 8x+b
Now we need to find b by using another point from this linear function.
We can use the point (2,24).
Plug this point into the equation y = 8x+b
- 24 = 8(2)+b
- 24 = 16 + b
- b = 8
We have now found the equation of the linear function: y = 8x+8
Answer:
49
Step-by-step explanation:
a+b/2xh
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<u>Methods to solve rational equation:</u>
Rational equation:
A rational equation is an equation containing at least one rational expression.
Method 1:
The method for solving rational equations is to rewrite the rational expressions in terms of a common denominator. Then, since we know the numerators are equal, we can solve for the variable.
For example,
![\frac{1}{2}=\frac{x}{2}\Rightarrow x=1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7Bx%7D%7B2%7D%5CRightarrow%20x%3D1)
This can be used for rational equations with polynomials too.
For example,
![\frac{1+x}{x-3}=\frac{4}{x-3}\Rightarrow(1+x)=4 \Rightarrow x=3](https://tex.z-dn.net/?f=%5Cfrac%7B1%2Bx%7D%7Bx-3%7D%3D%5Cfrac%7B4%7D%7Bx-3%7D%5CRightarrow%281%2Bx%29%3D4%20%5CRightarrow%20x%3D3)
When the terms in a rational equation have unlike denominators, solving the equation will be as follows
![\frac{x+2}{8}=\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B2%7D%7B8%7D%3D%5Cfrac%7B3%7D%7B4%7D)
![\Rightarrow\frac{x+2}{1}=\frac{3\times8}{4}\Rightarrow{x+2}=2\times3](https://tex.z-dn.net/?f=%5CRightarrow%5Cfrac%7Bx%2B2%7D%7B1%7D%3D%5Cfrac%7B3%5Ctimes8%7D%7B4%7D%5CRightarrow%7Bx%2B2%7D%3D2%5Ctimes3)
![\Rightarrow{x+2}=6\Rightarrow x=6-2\Rightarrow x=4](https://tex.z-dn.net/?f=%5CRightarrow%7Bx%2B2%7D%3D6%5CRightarrow%20x%3D6-2%5CRightarrow%20x%3D4)
Method 2:
Another way of solving the above equation is by finding least common denominator (LCD)
![\frac{x+2}{8}=\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B2%7D%7B8%7D%3D%5Cfrac%7B3%7D%7B4%7D)
Factors of 4: ![1\times2\times2](https://tex.z-dn.net/?f=1%5Ctimes2%5Ctimes2)
Factors of 8: ![1\times2\times2\times2](https://tex.z-dn.net/?f=1%5Ctimes2%5Ctimes2%5Ctimes2)
The LCD of 4 and 8 is 8. So, we have to make the right hand side denominator as 8. This is done by the following step,
![\Rightarrow\frac{x+2}{8}=\frac{3}{4}\times{2}{2}](https://tex.z-dn.net/?f=%5CRightarrow%5Cfrac%7Bx%2B2%7D%7B8%7D%3D%5Cfrac%7B3%7D%7B4%7D%5Ctimes%7B2%7D%7B2%7D)
we get,
![\Rightarrow\frac{x+2}{8}=\frac{6}{8}](https://tex.z-dn.net/?f=%5CRightarrow%5Cfrac%7Bx%2B2%7D%7B8%7D%3D%5Cfrac%7B6%7D%7B8%7D)
On cancelling 8 on both sides we get,
![\Rightarrow(x+2)=6\rightarrow x=6-2\rightarrow x=4](https://tex.z-dn.net/?f=%5CRightarrow%28x%2B2%29%3D6%5Crightarrow%20x%3D6-2%5Crightarrow%20x%3D4)
Hence, these are the ways to solve a rational equation.
Answer:
<u>a) 100m</u>
<u>b) 2m/s</u>
Step-by-step explanation:
a)==>> <u>2+4</u>+<u>6+8</u>+10(8) = 100m
b)==>> Variable "a" = change OVER time (
) = 8m/4s = 2m/s
The slope would be undefined, because it would be going straight vertical.