SOLUTION: please help i don't understand how to make the equations like this: write an equation of the line containing the given point and parallel to the given line (2,-4);9x-5y=6

Algebra ->  Linear-equations -> SOLUTION: please help i don't understand how to make the equations like this: write an equation of the line containing the given point and parallel to the given line (2,-4);9x-5y=6      Log On


   

Question 258322: please help i don't understand how to make the equations like this:
write an equation of the line containing the given point and parallel to the given line (2,-4);9x-5y=6
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
slope intercept form of the equation for a line is y = m*x + b where m is the slope and b is the y-intercept.

the given line is 9x - 5y = 6

that equation is in standard form.

to convert to slope intercept form, solve for y.

equation is:

9x - 5y = 6

subtract 9x from both sides of this equation to get:

-5y = -9x + 6

divide both sides of this equation by 5 to get:

-y = (-9/5)*x + (6/5)

multiply both sides of this equation by -1 to get:

y = (9/5)*x - (6/5)

you now have the equation in slope intercept form.

the slope is (9/5) and the y-intercept is -(6/5)

graph of this equation looks like this:

graph+%28+600%2C600%2C-5%2C5%2C-10%2C10%2C%289%2F5%29%2Ax-%286%2F5%29%29

that just gets you the graph of the line you want to be parallel to.

your line will be parallel to this line so the slope will be the same.

the slope intercept form of the equation for your line will be:

y = (9/5)*x + b

you do not know what b is but you can solve for b by substituting the x value of your point for x and the y value of your point for y and then solve for b.

your point that is on the line parallel to the given line is (2,-4).

that's in (x,y) coordinate form.

x = 2
y = -4

substitute these in the equation for your line that is parallel to the given line.

that equation is:

y = (9/5)*x + b

substitute 2 for x and -4 for y to get:

-4 = (9/5)*2 + b

simplify to get:

-4 = (18/5) + b

subtract (18/5) from both sides of the equation to get:

-4 - (18/5) = b

-4 is equivalent to -20/5 because if you divide -20 by 5, you get -4.

solve for b to get

b = (-20/5) - (18/5) = (-38/5)

equation for you line becomes:

y = (9/5)*x - (38/5) after you substitute (-38/5) for b.

graph of this equation in addition to the given line is shown below: