Collinear Points (6, -1), (2, 5), and (3, k)

[Tigertigre2000]

Collinear pionts lie on the same line. FInd the value of k for which the following points are collinear:

. . .(6, -1), (2, 5), (3, k)

I just don't understand what equation to use. I appreciate your helping me.

 

[stapel]

Hint: The slope between any two points on the same line will always be the same.

Eliz.

 

[Tigertigre2000]

So would you use (y2- y1)/( x2-x1) to get the slope of the pionts, or would you use another equation to get the slope?

I'm getting confused what i'm suppose to be doing, since my teacher keeps mentioning so many different equations.

 

[pka]

Collinear pionts lie on the same line. FInd the value of k for which the following points are collinear:
. . .(6, -1), (2, 5), (3, k).

You want the same slope determined by the points.
\(\displaystyle \
\frac{{\left( 5 \right) - \left( { - 1} \right)}}{{\left( 2 \right) - \left( 6 \right)}} = \frac{{\left( k \right) - \left( { - 1} \right)}}{{\left( 3 \right) - \left( 6 \right)}}.\)

 

[stapel]

So would you use (y2- y1)/( x2-x1) to get the slope of the pionts, or would you use another equation to get the slope?

To find the slope, yes, you should use the "slope" formula.

Eliz.

 

[Tigertigre2000]

The thing I was doing wrong as not setting them equal to each other.
Thanks I get it now.