SOLUTION: Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b (-6,7); 2x=9y+8

Question 454369: Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b
(-6,7); 2x=9y+8
Found 3 solutions by mananth, solver91311, ikleyn:
Answer by mananth(16949)   (Show Source): You can put this solution on YOUR website!
2x-9y=8
Find the slope of this line

-9y=-2x +8
Divide by -9
y = 0.22 x + -0.89
Compare this equation with y=mx+b
slope m = 0.22
The slope of a line parallel to the above line will be the same
The slope of the required line will be 0.22
m= 0.22 ,point (-6,7)
Find b by plugging the values of m & the point in
y=mx+b
7=-1.33+ b
b=8.33
m=0.22
Plug value of the slope and b
The required equation is y=0.22 x+8.33

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Your given equation has x and y on opposite sides of the equals sign, so the slope is simply the coefficient on x divided by the coefficient on y.

Parallel lines have identical slopes. So the slope of the line you are trying to find is the same as the slope of the line that is the graph of the given equation.

Using the information of a given point and a given slope, use the point-slope form of an equation of a line:

where are the coordinates of the given point and is the given/calculated slope.

Once you have inserted the values and done the indicated arithmetic, including distributing the slope value across the parenthetical binomial in the RHS, add the value of to both sides to complete the transformation to the slope-intercept form.

John

My calculator said it, I believe it, that settles it

Answer by ikleyn(53547)   (Show Source): You can put this solution on YOUR website!
.
Write an equation of the line containing the given point and parallel to the given line.
Express your answer in the form y=mx+b
(-6,7); 2x=9y+8
~~~~~~~~~~~~~~~~~~~~~~~~

        The solution and the answer in the post by @mananth both are incorrect.
        They are incorrect, since @mananth permanently rounds rational fractions to decimal fractions
        even when it is not allowed and ruins the precise form of equations.

        So, I came to make the job in a right way as it SHOULD be done.

Any line parallel to 2x = 9y + 8 has the form 2x = 9y + c, (1) where 'c' is a real constant. To find 'c', we simply insert coordinates (-6,7) into equation (1) 2*(-6) = 9*7 + c, -12 - 63 = c, c = -75. Thus equation (1) takes the form 2x = 9y - 75. (2) To get the form y = mx + b, we express 'y' from equation (2) y = + , or, which is the same y = + 8. (3) So, the slope of the sough line is m = and its equation is y = + 8.

Solved correctly.

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