A line has a slope of 2 and includes the points (1,k) and (3, - 1). What is the value of k?

Question

i hate life

Answer 1

Slope is sometimes called "rise over run" because it is the difference between y-values divided by the difference between x-values,

 

If the slope = 2, then:

   2 = (y₂ - y₁) / (x₂ - x₁)

   2 = (-1 - k) / (3 - 1)

 

   2 = -(k+1) / 2                    [factor out (-1)]

   -4 = k+1                       [multiply both sides by (-2)]            

    -5 = k                         [subtract 1 from both sides]

 

Check (very important):

   The equation of the line (in slope-intercept form) is:

          y = 2x + b                [y = mx+b]

          -1 = 2(3) + b             [use point (3,-1)]

          -7 = b

      The equation of the line is: y=2x-7

   Is (1,k) on the line? 

        k = 2(1) - 7

        k = -5    ? yes

   Is (3,-1) on the line?

       -1 = 2(3) - 7   ?

       -1 = -1   ?yes

Answer 2

Slope = the difference between the two y coordinates, over the corresponding difference between the two x coordinates. The diff between the x's is 2, which means the diff between the y's must be 4, since 4/2 is 2.

 

So what can you plug in for k that makes the diff between the y's equal 4?