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Mathematics

1 answer:

vagabundo [1.1K]1 year ago

3 0

Answer:

Step-by-step explanation:

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What is an equation of the line that passes through (2,2) and is parellel to the line y=7x

laila [671]

Answer:

Therefore, equation of the line that passes through (2,2) and is parellel to the line $y=7x$ is $y=7x-12$

Step-by-step explanation:

Given:

a line $y=7x$

To Find:

Equation of line passing through ( 2, 2) and is parellel to the line y=7x

Solution:

$y=7x$ ...........Given

Comparing with,

$y=mx$

Where m =slope

We get

$Slope = m = 7$

We know that parallel lines have Equal slopes.

Therefore the slope of the required line passing through (2 , 2) will also have the slope = m = 7.

Now the equation of line in slope point form given by

$(y-y_{1})=m(x-x_{1})$

Substituting the points and so we will get the required equation of the line,

$(y-2)=7(x-2)=7x-14\\\\y=7x-12......Equation\ of\ line$

Therefore, equation of the line that passes through (2,2) and is parellel to the line $y=7x$ is $y=7x-12$

4 0

2 years ago

Rewrite in Polar Form....<br> x^(2)+y^(2)-6y-8=0

skad [1K]

$\bf x^2+y^2-6y-8=0\qquad 
\begin{cases}
x^2+y^2=r^2\\\\
y=rsin(\theta)
\end{cases}\implies r^2-6rsin(\theta)=8
\\\\\\
\textit{now, we do some grouping}\implies [r^2-6rsin(\theta)]=8
\\\\\\\
[r^2-6rsin(\theta)+\boxed{?}^2]=8\impliedby 
\begin{array}{llll}
\textit{so we need a value there to make}\\
\textit{a perfect square trinomial}
\end{array}$

$\bf 6rsin(\theta)\iff 2\cdot r\cdot \boxed{3\cdot sin(\theta)}\impliedby \textit{so there}
\\\\\\
\textit{now, bear in mind we're just borrowing from zero, 0}
\\\\
\textit{so if we add, \underline{whatever}, we also have to subtract \underline{whatever}}$

$\bf [r^2-6rsin(\theta)\underline{+[3sin(\theta)]^2}]\quad \underline{-[3sin(\theta)]^2}=8\\\\
\left. \qquad \right.\uparrow \\
\textit{so-called "completing the square"}
\\\\\\\
[r-3sin(\theta)]^2=8+[3sin(\theta)]^2\implies [r-3sin(\theta)]^2=8+9sin^2(\theta)
\\\\\\
r-3sin(\theta)=\sqrt{8+9sin^2(\theta)}\implies r=\sqrt{8+9sin^2(\theta)}+3sin(\theta)$

3 0

2 years ago

Find the slope of the line passing through the points (-6,7) and (-8,5)

kykrilka [37]

Answer:

Slope = 1

Step-by-step explanation: