Question

Write the equation of the line that passes through points C and D
C(-1,4) and D(6,-6)

Answer 1

First find the slope of the line through the two points.


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



m = (-6-4)/(6-(-1))



m = (-6-4)/(6+1)



m = (-10)/7



m = -10/7



So the slope of the line that passes through the two points is -10/7


Now use y = mx+b along with (x,y) = (-1,4) to find the equation of the line.



\[\Large y = mx+b\]


\[\Large 4 = \left(\frac{-10}{7}\right)\left(-1\right)+b\]


\[\Large 4 = \frac{10}{7}+b\]


\[\Large 4-\frac{10}{7} = b\]


\[\Large \frac{18}{7} = b\]


\[\Large b = \frac{18}{7}\]


So the equation of the line is \[\Large y = -\frac{10}{7}x+\frac{18}{7}\]