How to solve the equation of this line

If you can, explain the steps necessary to solve this problems and others like it.
Write an equation of the line that passes through the point (6,-5) and is parallel to the line whose equation is 2x-3y=11

First, rewrite 2x - 3y = 11 into slope-intercept form y = mx + b

Subtract 2x from both sides:

-3y = -2x + 11

Divide through by -3:

y = (2/3)x - 11/3

The slope of the line is 2/3. A parallel line has the same slope.


The equation for the new line starts as:

y = (2/3)x + b where b is the y-intercept

To sove for b, substitute the x and y values of the point you've been given:

-5 = (2/3)6 + b

Multiply it out:

-5 = 4 + b

Subtract 4 from both sides:

b = -9

The full equation for the new line is:

y = (2/3)x - 9

It looks quite complicated but it's not really! If it is parallel to the line 2x-3y=11, then the gradients of the two lines will be equal. So rearrange the equation ----> 2x-11=3y -----> y=(2/3)x - (11/3).
So the gradient of your line is 2/3. Okay, now the standard equation for any line is y=mx+c, right? And m is the gradient. So then you plug in x and y coordinates of the point it passes through ----> y=(2/3)x+c -----> -5 = (2/3)*6 + c, Solve for c, which gives c = -9
Therefore, the equation of the line: y = (2/3)x - 9
Hope that helps!

let the equation which parallel to given equation is
2x-3y= k

then this equation passes throw (6,-5),this point satishfied by last equation so put the value of x and y for finding the value of k.
We get
2*6-3*(-5)=k,
12+15 =k
27=k, putting the value of k in above equation,we get
2x-3y=27
this is required equation.

write the first equation in the form of y=mx+b
-3y=-2x+11
y=2/3x-11/3 so the second equation line must have a slope of 2/3 to be parallel. now use the
y=mx+b to get a new equation for the line passing thru 6,-5

-5=2/3(6)+b
-5=4+b
b=-9 so the equaation is y=2/3x-9 or y-2/3x=-9 or -3y+2x=27 ==> 2x-3y=27

Keep the coefficients of the variables the same:

2x - 3y = C

Plug in values for x and y and solve for C

x = 6
y = -5

2 * (6) - 3 * (-5) = C
12 + 15 = C
27 = C

So, the equation of the line is:

2x - 3y = 27