Find the slope of the line that passes through (7, 8) and (10, 10). Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answer 1

Take the difference in y coordinates and divide that by the difference in the x coordinates. That's the slope, sometimes called the "rise over run" For a straight line or a linear function the slope is a constant

(10-8)/(10-7) = 2/3 = slope

the line is

y-h = m(x-k) where m=2/3 and (k,h) = (10,10) or either point

to get y-10 = (2/3)(x-10)

3y -30 = 2x-20

2x-3y = -10

or use (k,h) as (7,8)

y-8 = (2/3)(x-7)

3y-24 = 2x-14

2x-3y = -10

or if you write it in y=mx + b form

it's y=(2/3)x + 10/3 where 10/3 is the y-intercept and 2/3 = slope

In this form, take the derivative of (2/3)x + 10/3

to get y' = 2/3, the derivative is the slope