Write an equation in slope intercept form of the line with the given parametric equations x=8t+3 y=9t+3

Mathematics

1 answer:

Novosadov [1.4K]3 years ago

4 0

Answer:

The slope intercept equation of the line is:

y = (9/8)x - (3/8)

Step-by-step explanation:

- They give us 2 parametric equations to arrive at y = mx + b (Slope intersection equation)

1. X = 8t + 3

2. Y = 9t + 3

- We first convert in terms of t to compare both equations:

1. x = 8t + 3

x - 3 = 8t

t = (x - 3) / 8

- Same for the following:

3. y = 9t + 3

y - 3 = 9t

t = (y - 3) / 9

- Now equating by comparing both equations, we will find y:

(x - 3) / 8 = (y - 3) / 9

9x -27 = 8y -24

9x - 3 = 8y

- Clearing and comparing both parameters gives us:

y = (9/8)x - 3/8

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$\text{The scientific notation:}\\\\a\times10^n\\\\1\leq a$

$a.\\(5\times10^3)\times(3.5\times10^{-1})=(5\times3.5)\times(10^3\times10^{-1})\\\\=15.75\times10^{3+(-1)}=15.75\times10^2=1.575\times10\times10^2\\\\=1.575\times10^{1+2}=\boxed{1.575\times10^3}$

$b.\\(8\times10^2)\div(4\times10^3)=(8\div4)\times(10^2\div10^3)=2\times10^{2-3}\\\\=\boxed{2\times10^{-1}}$

$c.\\(6\times10^{-3})^2=6^2\times(10^{-3})^2=36\times10^{-3\cdot2}=36\times10^{-6}=3.6\times10\times10^{-6}\\\\=3.6\times10^{1+(-6)}=\boxed{3.6\times10^{-5}}$