Find the slope of the line that passes through (8, 9) and (1, 6)

Question

Find the slope of the line that passes through (8, 9) and (1, 6).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answer 1

Hi Morgan! Remember that the slope is rise/run. Rise is how much the y-coordinate changes and run is how much the x-coordinate changes. In this case, y rises from 6 to 9, so rise = 3. x runs from 1 to 8, so run = 7. So, your slope is 3/7.

Answer 2

(8,9) and (1,6) have a line through them with the equation

(y-y1) = m(x-x1) with m=slope = (9-6)/(8-1) = 3/7

y- 9=(9-6)/(8-1) times x-8

y-9 = (3/7)(x-8) in point slope form

y = 3x/7 -24/7 +9

y =3x/7 -24/7 +63/7

y = 3x/7 +39/7 in slope intercept form

7y = 3x+39

3x-7y =-39 in standard form

3x-7y +39 = 0 in general form

Answer 3

To find the slope of a line passing through two given points use m = (y₂-y₁)/(x₂-x₁). Think of this as change in y over change in x (or rise over run).

Let's say you designate (8, 9) as P₁ and (1, 6) as P₂.

Then m = (6 - 9) / ( 1- 8) = -3/-7 = 3/7.

If you do it with (1,6) as P₂:

m= (9 - 6) / (8 -1) = 3/7.

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