How do you write the equation in point slope form given (–2, 15), (9, –18)?

2 Answers
Feb 22, 2016

y-15=-3(x+2)y15=3(x+2)

Explanation:

Slope:
color(white)("XXX")m=(Delta y)/(Delta x) = (15-(-18))/(-2-9)=33/(-11) = -3

The general slope-point form for a line with slope m through a point (barx,bary) is
color(white)("XXX")y-bary=m(x-barx)

Using (-2,15) for (barx,bary)
color(white)("XXX")y-15=-3(x+2)

Feb 22, 2016

Equation of the line is 3x+y=9

Explanation:

Equation of the line between two points say (x_1,y_1) and (x_2,y_2) in point slope form is given by

(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1), where both LHS and RHS represent slope of the line,

Hence equation of the line between (-2,15) and (9,-18) is given by

(y-15)/(x-(-2))=((-18)-15)/(9-(-2)) i.e.

(y-15)/(x+2)=(-18-15)/(9+2) or (y-15)/(x+2)=(-33)/11=-3 i.e.

(y-15)=-3*(x+2) i.e.

(y-15)=--3x-6

or 3x+y=-6+15=9

As such, equation of the line is 3x+y=9