Math Graphing Question

Question

Find a if the point (3,a) is on the line that passes through (-2,7) and (5,-3).

Answer 1

We need to find the equation of the line thought the 2 known points and then plug in the unknown point.  First, we need the slope:

 

m = (y1-y2)/(x1-x2)

m= (7 - -3) / (-2 -5)

m= -10/7

 

Now we can find the equation of the line in point slope form:

 

y-y1 = m(x-x1)

y - 7 = -10/7*(x - -2)

y-7 = -10/7* (x+2)

7y - 49 = -10(x+2)

7y - 49 = -10x - 20

7y = -10x - 20 + 49

7y = -10x + 29

y = -10x/7 + 29/7

 

Finally, we can plug in x=3 to find the value of a in (3,a):

 

a = -10(3)/7 + 29/7

a = -30/7 + 29/7

a = -1/7