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Answer: y=2/3x+7/3

Step 1: Turn this equation into slope intercept form

-2x+3y=-4

*add 2x on both sides*

-2x+3y= -4
+2x +2x
___________
3y= 2x-4

*divide each number/coefficient by 3*

3y/3 = 2x/3 -4/3

y=2/3x-4/3

Knowing this will only tell us the slope. When it is parallel, the slope remains the same. So, the slope for this equation will stay 2/3

Step 2: Substitute the point into the current equation

As of now the equation is y=2/3x+b. In order to find the y-intercept, substitute the given point into this equation.

y=2/3x+b

3=2/3(1)+b

3=2/3+b
-2/3 -2/3
_________
2 1/3 =b

It is mathematically preferred to leave this in improper form. So we will turn 2 1/3 into 7/3

Step 3: Input information

Now that we know that the slope is 2/3 and the y-intercept is 7/3, we can turn this into an equation:

y=2/3x+7/3

Hope this helps comment below for more questions :)

2x+3y=7 or 2x-3y= -11 represents a line parallel to the  given line.

What is the equation of line?

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x, y to form an algebraic equation, which is referred to as an equation of a line. Using the equation of any line, we can find whether a given point lies on the line or not. the equation of line is a linear equation with a degree of one. Let us understand more about the different forms of the equation of a line and how to find the equation of line.

According to the question,

-2x+3y= -4,

which is Ax + By = C

A=-2 B=3 C=-4

m(slope)= -A/B

m= -(-2)/3

m= 2/3

y-y1= m (x-x1)

y-3= 2/3 (x-1)

Multiply by 3 cancels out the fraction

3y-9= 2 (x-1)

Distributive property

3y-9= 2x-2

-2x+3y-9= -2

From here it could go 2 ways:

1. -2x+3y= 7

or

2. 2x-3y+9= -2

so

2x-3y= -11

Hence , 2x+3y=7 or 2x-3y= -11 represents a line parallel to the  given line.

To learn more about equation of line from here

https://brainly.com/question/2564656

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