Question

which equation represents a line parallel to the line whose equation is -2x+3y=-4 and passes through the point (1,3)?

Answer 1

The slope of the line has to be the same the the equation given to be parallel.

The slope of the line given is... 2/3.

If the line passes through point (1,3) then...

3=2/3(1)+b

b=2 1/3

answer: y=2/3x+2 1/3

Answer 2

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 :)