Question

The equation of the line that goes through the points (5,9) and (6,3) can be written in the form y=mx+b, where is m? where is b?

Answer 1

find the gradient (slope) which is rise/run

\[m = (y _{2} - y _{1})/(x _{2} -x _{1})\]

let (5,9) be the 2 point (6, 3) be the 1 point

m = (9 - 3)/(5 - 6)

m = -6

use the point slope formula
\[y - y _{1} = m(x - x _{1})\]

y - 3 = -6(x - 6)

expand and simplify

y = -6x + 39

Answer 2

m is the slope of the line, b is the y-intercept, where x = 0 the point is (0, 39)