Expert: Bobby Soltani - 1/26/2005

Question
Hi! Ok i have this test tomorrow so i really need your help and fast! Please. Ok i want to know how to change a whole number into a fraction so i can mulitiply.  For example in the problem (-2,4) (-6,5), i can get the slope, and then i dont know what to do please help.
                              Rebecca


Answer
Hi Rebecca,

Here is how to get the equation for line from the two points (-2,4) and (-6,5)

The equation for a line is
y - y1 = m(x-x1)
where m is the slope, and (x1,y1) is any point on the line.

Let's first find the slope

m = (y2-y1)/(x2-x1)
let (-6,5) be point 2 so that x2=-6 and y2 = 5
Then, x1=-2 and y1=4

m = (5-4)/(-6-(-2))
m = (1)/(-6+2)
m = 1/-4
m = -1/4

now plug m,y1,and x1 into the equation.
y-4 = (-1/4)(x-(-2))
y-4 = (-1/4)(x+2)
multiply the -1/4 by the x and the 2 in the parenthesis
y-4 = -(1/4)x - 2/4
y-4 = -(1/4)x - 1/2
add 4 to both sides
y = -(1/4)x - 1/2 + 4
add the fraction and the 4
y = -(1/4)x - 1/2 + 8/2
since we want the same denominators, we multiply the 4 by 2/2 to get 8/2
add the numberators -1 + 8

y = (-1/4)x + 7/2

That's it.  Let me know if you have questions.

Bobby