Write an equation for a line parallel to x+15=-5y passing through (0,4)

- anonymous

Write an equation for a line parallel to x+15=-5y passing through (0,4)

- katieb

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- mathstudent55

Parallel lines have the same slope,
First, you need to find the slope of the given line, then use that slope for the new line.
To find the slope of the given line, solve x + 15 = -5y for y. Then put it in slope-intercept form, which is y = mx + b. m is the slope.
Second, the equation of a line with slope m that passes through point (x1, y1) is
y - y1 = m(x - x1)
Try it, and ask for help if you need it.

- anonymous

Thanks,I need help putting x=15=-5y into slope intercept form

- mathstudent55

First, switch the sides, so you start with -5y on the left side.

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- mathstudent55

Next, the only thing happening to the y is that it is being multiplied by -5. How do you undo a multiplication?

- whpalmer4

\[x+15 = -5y\]Divide both sides by -5 to give\[-\frac{x}{5} -3 = y\]Now switch the sides.

- anonymous

Umm I think that by dividing?? So will that mean that I'm dividing 15 by -5y??

- mathstudent55

Correct, divide both sides by -5

- anonymous

So then what will happen next to the x??

- mathstudent55

-5y = x + 15
Divide -5y by -5
Divide x by -5
Divide 15 by -5

- anonymous

OK I got -5-3=y ..?..?..?

- anonymous

wait wait! I checked it and it actually its suppose to be y=-1/5-3

- mathstudent55

-5y/(-5) = x/(-5) + 15/(-5)
y = -(1/5)x - 3

- mathstudent55

Remember to include the x on the right side.

- anonymous

YESSSSSSS!!!!!

- mathstudent55

Since the original equation is now written in slope-intercept form, y = mx + b, you can read the slope directly. It's the number multiplying x, which is m.
m = ?

- anonymous

m=4 so then that will mean that the final answer will be y=-1/5x+4 xD

- mathstudent55

Where did you get a 4 from y = -(1/5)x - 3?

- mathstudent55

Remember, the slope-intercept form is y = mx + b, where m, the number multiplying x, is the slope.

- anonymous

ohh ok then my bad

- mathstudent55

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- mathstudent55

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- mathstudent55

What is m, the slope?

- anonymous

-1/5

- mathstudent55

Correct. Now you know the given line has a slope of -1/5. The line that is parallel to it also has that slope becasue parallel lines have equal slopes.
Now we start on the second part of this problem.
What is the equation of the line that has slope -1/5 and passes through (0, 4)?

- anonymous

4=-1/5(0)+b which will then turn into 4=0+b

- mathstudent55

In the slope-intercept form of the equation of a line,
y = mx + b,
m = slope (you already know this)
b = the y-intercept
Correct. b = 4, since the point you were given, (0, 4) is on the y-axis, so that is the y-intercept.

- anonymous

Then I will do inverse operation and subtract 0 from both sides making it be 4=b

- mathstudent55

Now you know your new equation has m = -1/5 and b = 4.
All you need to do is write
y = mx + b
and replace m with -1/5 and b with 4

- mathstudent55

Correct, b = 4

- anonymous

and it will end up being y=-1/5x+4

- mathstudent55

You are correct. Great work!

- anonymous

OMG thank you so much your the best!!=D will you mind helping me with another type of problem.I have a quiz on Wednesday and I'm practicing right now.

- mathstudent55

I certainly will help. Just pls start a new post.

- anonymous

OK then (:

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