Please help with this math question! (Straight line equation)

Find the equation of the straight line through A and B. Write your answer in the form ax+by=c where a, b and c are whole numbers.

Coordinates of

A (-3,-2)
B (4,1)

Image:http://www.freeimagehosting.net/4iji7

Thanks a lot!

1. first find the slope of the equation, dividing the difference in y by the difference in the two x values, like this:
-2-1 <--- difference in y values
------- divided by
-3-4 <--- difference in x values

which equals

-3/-7, or 3/7 as your slope.

2. now multiply 3/7 by one of the x values, lets use 4. this gets 12/7. the difference from 12/7 to the y value of that point is -5/7 so that is our y intercept

this gives us an equation of y=3/7x-5/7

3. since we need it in ax+by=x form, subtract 3/7x from both sides of the equation to get it onto the left side:
-3/7x+y=-5/7

4. since we need the numbers in whole number form, multiply everything in the equation by 7. this will get rid of the fractions:
-3x+7y=-5 is your final answer :)

A (-3,-2)
B (4,1)

m = (y2-y1) / (x2-x1) = (-2 -1) / (-3 -4) = -3/-7 = 3/7
To find equation substitute into
y -y1 = m( x -x1)
y - 1 = 3/7 ( x-4)
7y -7 = 3(x-4)
7y -7 = 3x -12
-3x +7y = -5
or 3x -7y = 5
cf ax +by = c where a = 3 , b =-7 & c=5