# Thread: find equation in the form of ax+by+c=0

1. ## find equation in the form of ax+by+c=0

hello,

im not to sure how to work out this question:

the straight line L passes through the point P(-3,6) and the point Q(1,-4)

i) Find an equation for L in the from of ax+by+c=0 wherea,b and c are integers.

im not too sure how i would complete this question so could someone help me please so i know how to get going.

thanks!!

2. ## Re: find equation in the form of ax+by+c=0

Originally Posted by andyboy179
hello,

im not to sure how to work out this question:

the straight line L passes through the point P(-3,6) and the point Q(1,-4)

i) Find an equation for L in the from of ax+by+c=0 wherea,b and c are integers.

im not too sure how i would complete this question so could someone help me please so i know how to get going.

thanks!!
If a straight line passes through $P_1(x_1, y_1)$ and $P_2(x_2, y_2)$ the equation of the line can be determeined by the two-point-equation of the line:

$\frac{y-y_1}{x-x_1} = \underbrace{\frac{y_2 - y_1}{x_2 - x_1}}_{\text{this is the slope}}$

Plug in the coordinates of the two points.

Re-write the equation until you've got it in the correct form.

You should come out with 5x+2y+3=0

3. ## Re: find equation in the form of ax+by+c=0

im confused i did the y2-y1/x2-x1 and got -10/4 i dont understand how to go from there

4. ## Re: find equation in the form of ax+by+c=0

Originally Posted by andyboy179
im confused i did the y2-y1/x2-x1 and got -10/4 i dont understand how to go from there
Math Forum - Ask Dr. Math

5. ## Re: find equation in the form of ax+by+c=0

Hi Andy,

You're right, that is a really confusing question! Let me see if I can help. I'm not really a huge math person, but I learned how to solve problems like this in Algebra.

Not to confuse you, but I think writing an equation in slope-intercept form (y=mx+b) makes it easier. Then you can just switch around the numbers to put it in the right format.

y = mx + b

If you plug in a y-variable for y (like 6), your slope (-10/4 or -5/2, simplified) for m, and an x-value for x (like -3), you can solve for the slope-intercept (b). Once you solve for b you just write the equation as:

y = -5/2x + b(whatever that is!)

From there you just set x and y on the same side (subtract x from y). This problem is all fractions, so you can find a number to multiply the whole equation by to get tidy whole numbers (I don't really know if this is necessary...or what you're supposed to do...but it sure looks better).

That's all I've got, but Teens Get Math Help at Alleyoop (I think it's just called Alleyoop) has a 24 hour online tutoring service you can use. I'm pretty sure the first session's free, but you'll have to check out the site. They also have really cool videos that explain everything about math.

Hope that helps!

Hannah