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emmainna [20.7K]
2 years ago
10

Write in slope-intercept form the equation of the line that is parallel to the line y=2/3x-6 and passes through the point (3,3)

Mathematics
1 answer:
ser-zykov [4K]2 years ago
6 0

Answer: y=2/3x+1

Step-by-step explanation:

y=2/3x-6

y=2/3x+b ==> Parallel to y=2/3x-6 since they both have the same slope

3=2/3 (3)+b

3=2*3/3 +b

3=6/3 +b

3=2+b

b=1

y=2/3x+1

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Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? If it is a direct o
inn [45]

Answer: neither direct variation nor inverse variation.


Explanation:


1) The relation between two variables, y and x, is a direct variation if and only if the quotient between them, y/x, is constant. This is: y / x = k or, equivalently, y = kx.


Note that if y / x is constant, x / y is also constant.


In a direct variation, when x increases, y increases, and when x decreases, y decreases.


2) The relation between two variables, y and x, is an inverse variation if and only if their product, y×x is constant. This is: y × x = k or, equivalently y = k /x or x = k / y.


In an inverse variation when one of the variables increases the other decreases.


3) Writhe the given table and study whether the conditions for direct or inverse variation are met:

x      y              y/x                             y×x

-6    -72           -72/(-6) = 12             (-6)(-72) = 432

-4    -47           -47 / (-4) = 11.75       (-4)(-47) = 188

-3    -36           -36 / (-3) = 12           (-3)(-36) = 108

1       12             12 / 1 = 12                (1)(12) = 12


Conclusions;


a) Since neither y / x nor y×x have the same result for every pair, the relation is neither direct nor inverse.


b) Note that if the third pair were (-4, -48) instead of (-4, -47), y / x would be 12, which make a direct variation. In this case the function that modeled it would be:

         y = 12x.

8 0
3 years ago
Find a general linear equation Ax+By+C=0 of the straight line that passes through the point (1,1) and has slope 1/5.
dedylja [7]
\bf \begin{array}{lllll}
&x_1&y_1\\
%   (a,b)
&({{ 1}}\quad ,&{{ 1}})\quad 
%   (c,d)

\end{array}
\\\quad \\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies\cfrac{1}{5}
\\ \quad \\
% point-slope intercept
y-{{ y_1}}={{ m}}(x-{{ x_1}})\qquad 
\begin{array}{llll}
\textit{plug in the values}\\
\textit{and move everything to}\\
\textit{the left-side}
\end{array}\\
\qquad \uparrow\\
\textit{point-slope form}
5 0
3 years ago
Can you Please help me
a_sh-v [17]

Answer:

The slope is 4 because \frac{20-12}{5-3} = \frac{8}{2} = 4.

8 0
3 years ago
Which best describes the incenter of a triangle?
sineoko [7]

Answer:

The statement that best describes the incenter of a triangle is that, it is the point where the three angle bisectors of the triangle intersect. In geometry, an incenter of a triangle is described as the triangle center.

Step-by-step explanation:

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6 0
3 years ago
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Frank invests $1,000 in simple interest investment account that pays 8% a year. After a number of years, he withdraws his balanc
IceJOKER [234]

Answer:

15\ years

Step-by-step explanation:

we know that

The simple interest formula is equal to

I=P(rt)

where

A is the Final Investment Value

I is the amount of money in Interest  

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

t=?\ years\\ P=\$1,000\\ A=\$2,200\\r=0.08

<em>Find the interest I</em>

I=A-P=\$2,200-\$1,000=\$1,200

substitute in the formula above

\$1,200=\$1,000(0.08t)

Solve for t

t=1.2/0.08=15\ years

6 0
3 years ago
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