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What is the equation of the line that passes through (-2,3) and is parallel to 2x+3y=6?

Vsevolod [243]

Answer:

Step-by-step explanation:

$\bold{METHOD\ 1:}$

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

Let $k:y=m_1x+b_1,\ l:y=m_2x+b_2$

then

$l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

We have the equation of a line:

$2x+3y=6$

Convert to the slope-intercept form:

$2x+3y=6$ subtract 2x from both sides

$3y=-2x+6$ divide both sides by 3

$y=-\dfrac{2}{3}x+2\to m_1=-\dfrac{2}{3}$

therefore the slope is $m_2=-\dfrac{2}{3}$

Put the value of the slope and the coordinates of the point (-2, 3) to the equation of a line:

$3=-\dfrac{2}{3}(-2)+b$

$3=\dfrac{4}{3}+b$ subtract 4/3 from both sides

$\dfrac{9}{3}-\dfrac{4}{3}=b\to b=\dfrac{5}{3}$

Finally:

$y=-\dfrac{2}{3}x+\dfrac{5}{3}$

Convert to the standard form (Ax + By = C):

$y=-\dfrac{2}{3}x+\dfrac{5}{3}$ multiply both sides by 3

$3y=-2x+5$ add 2x to both sides

$2x+3y=5$

$\bold{METHOD\ 2:}$

Let $k:A_1x+B_1y=C_1,\ l:A_2x+B_2y=C_2$ .

Lines k and l are parallel iff

$A_1=A_2\ \wedge\ B_1=B_2\to\dfrac{A_2}{A_1}=\dfrac{B_2}{B_1}$

We have the equation:

$2x+3y=6\to A_1=2,\ B_1=3$

then the equation of a line parallel to given lines has the equation:

$2x+3y=C$

Put the coordinates of the point (-2, 3) to the equation:

$C=2(-2)+3(3)\\\\C=-4+9\\\\C=5$

Finally:

$2x+3y=5$

4 0

3 years ago

If m>BFC = 8x+13 and m

deff fn [24]

Answer:

12x - 73

Step-by-step explanation:

DFE + CFD = 12x + 7

DFE + 90 = 12x + 7

DFE = 12x + 7 - 90

DFE = 12x - 83

therefore

DFE = AFB ( vertically opposite angles are equal)

AFB = 12x - 83

7 0

3 years ago

A group of employees bought a get-well gift for a coworker. The gift cost $46.06. If there are 22 employees in the group, how mu

soldi70 [24.7K]

Assuming they all contribute the same amount, then each would need to give $2.09, while one would have to give $2.10

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3 years ago

show that any binary integer is at most four times as long as the corresponding decimal integer. for very large numbers, what is

makkiz [27]

It has been shown that any binary integer is at most four times as long as the corresponding decimal integer.

<h3>What is the binary code?</h3>

The binary code is a method of expressing numbers that makes use of one and zero. It is the method in which the computer encodes data. The data must be transformed into zeros and ones before they can be encoded.

For instance, the number 8 is (1000)2. This shows that any binary integer is at most four times as long as the corresponding decimal integer.

Learn more about binary integer:brainly.com/question/14866711

#SPJ4

4 0

1 year ago

Xiao's teacher asked him to rewrite the sum 60+90 the product of the GCF of the two numbers and a sum. Axial wrote 3(20+30). Wha

LuckyWell [14K]

60 + 90

GCF = 30

(30 * 2) + (30 * 3) = 30(2 + 3) <== the correct way

The mistake Axial made was he did not pick the greatest common factor...he picked 3 instead of 30.

4 0

3 years ago

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