Find k if the line y = kx-5 passes through the point ( -2,3)

Question

Hi, I need help with solving the question. 

Answer 1

The line y=kx-5 is given in slope-intercept form [y=mx+b, where m is slope and (0,b) is the y-intercept].

 

The value k is the slope of the line.  The -5 is the y-intercept, the point (0,-5).

 

The problem is to find the slope (k, or m) of a line that has y-intercept of (0,-5) and goes through the point (-2,3).

 

Also, note that points have the form (x,y).

 

So,

      y = kx - 5

      3 = k*(-2) - 5           [use values (-2,3) for (x,y)]

      3 = -2k - 5              [re-write]

      8 = -2k                 [add 5 to both sides]

      -4 = k                 [divide both sides by (-2)]

 

The equation of the line is:

     y = -4k - 5