finding slope of line determined by (4, 3) and (3, 2)

[erinlyn]

ok, so i understand that the intercept format is y=mx+b, but i need to know how to start. the question is:

"find the slope of the determined points (4,3) , (3,2)".

i know it is suppossed to be y=mx+b but do i substitute those numbers in, for example making it y=4+3 ? or is it 3y=x+4 ?

 

[jwpaine]

For two ordered pairs: \(\displaystyle \L (x_1, y_1), (x_2, y_2)\)

slope = m = \(\displaystyle \L \frac{y_2 - y_1}{x_2 - x_1}\)

If you have the ordered pairs: (4,3) , (3,2), than your slope = m = \(\displaystyle \L \frac{2-3}{3-4} = \frac{-1}{-1} = 1\)

To setup the equation:

y = mx + b:
Solve for b:

(3) = (1)(4) + b
3 = 4 + b
b = -1

Thus y = x - 1


Moreover, using the point-slope form for the equation of a line:

\(\displaystyle \L y - y_1 = m(x - x_1)\)

\(\displaystyle \L y - 3 = 1(x - 4)\)

\(\displaystyle \L y = x - 1\)