Estimate: -√82<br> A. -9, 0<br> B. -9, 9<br> C. -9<br> D. 9

What is the equation of the line that is parallel to the line 2x+3y=-8 and passes through the point (2,-2)?

Leya [2.2K]

Equation of line passing through (2, -2) and parallel to 2x+3y = -8 is $y=\frac{-2 x}{3}+\frac{-2}{3}$

<h3><u>Solution:</u></h3>

Need to write equation of line parallel to 2x+3y=-8 and passes through the point (2, -2)

Generic slope intercept form of a line is given by y = mx + c

where "m" = slope of the line and "c" is the y - intercept

Let’s first find slope intercept form of 2x+3y=-8 to get slope of line

$\begin{array}{l}{2 x+3 y=-8} \\\\ {=>y=\frac{-2 x-8}{3}} \\\\ {\Rightarrow y=-\frac{2}{3} x-\frac{8}{3}}\end{array}$

On comparing above slope intercept form of given equation with generic slope intercept form y = mx + c,

$\text {for line } 2 x+3 y=-8, \text { slope } m=-\frac{2}{3}$

We know that slopes of parallel lines are always equal

So the slope of line passing through (2, -2) is also $m=-\frac{2}{3}$

Equation of line passing through $(x_1 , y_1)$ and having slope of m is given by

$\left(y-y_{1}\right)=\mathrm{m}\left(x-x_{1}\right)$

$\text { In our case } x_{1}=2 \text { and } y_{1}=-2$

Substituting the values in equation of line we get

$(y-(-2))=-\frac{2}{3}(x-2)$

$\begin{array}{l}{\Rightarrow y+2=\frac{-2 x+4}{3}} \\\\ {=>3(y+2)=-2 x+4} \\\\ {=>3 y+6=-2 x+4} \\\\ {3 y=-2 x-2}\end{array}$

$y=\frac{-2 x}{3}+\frac{-2}{3}$

Hence equation of line passing through (2 , -2) and parallel to 2x + 3y = -8 is given as $y=\frac{-2 x}{3}+\frac{-2}{3}$

7 0

3 years ago

Use the zeros and the labeled point to write the quadratic function

Anarel [89]

Answer:

y = 2x2 - 10x + 12

Step-by-step explanation:

5 0

2 years ago

If g(x)=2x+3 is a function,then find the unknown term in the following ordered pairs.

Dmitrij [34]

Answer:

a=2, b = 1, m=9

Step-by-step explanation:

i. 7 = 2a+3 -----> 4=2a---------> a=2

ii. -1 = 2b-3 -------> 2 = 2b ------> b = 1

iii. 2(3)+3 = m -------> 6+3 = m -------> m=9

Hope this helps!!! :D

5 0

3 years ago

Two positive, consecutive, odd integers have a product of 143.

zhannawk [14.2K]

Answer:

<em>The answer is 13</em>

Step-by-step explanation:

Two positive and consecutive old numbers are x and x - 2.

=> x(x - 2) = 143

=> x^2 - 2x - 143 = 0

=> x^2 + 11x - 13x - 143 = 0

=> x(x + 11) - 13(x + 11) = 0

=> (x + 11)(x - 13) = 0

=> x = -11 (invalid)

or x = 13 (valid), the remaining number is 13 - 2 = 11

=> The two numbers are 11 and 13, and the greater number is 13.

Hope this helps!

:)

7 0

3 years ago

Iris is a botanist who works for a garden that many tourists visit. the function f(s) = 2s + 25 represents the number of flowers

7nadin3 [17]

A function is said to be a composite function when a function is written in another function. The composite function that represents the number of flowers is f(w)=50w+25 and the number of flowers for 30 weeks is 1525.

Given that:

f(s)=2s+25

s(w)=25w

The number of flowers to bloom over w weeks is calculated using the following composite function: f(w)

f(s)=2s+25

Replace s with s(w)

f(s(w))=2(s(w))+25

Substitute (w)=25w

f(s(w))=2(25w)+25

f(s(w))=50w+25

Hence:

f(w)=50w+25

The units of the measurement of f(w) are flowers

The number of flowers for 30 weeks means:

w=30

So, we have:

f(w)=50w+25

f(30)=50 * 30+25

f(30)=1525

Hence, the number of flowers for 30 weeks is 1525

Learn more about composite functions here:brainly.com/question/10687170

#SPJ4

5 0

1 year ago

Estimate: -√82 A. -9, 0 B. -9, 9 C. -9 D. 9