Question

through (-2,3) and (5,-3) write the point slope form of the equation of the line through the given points

Answer 1

CONCEPT: Equation of a Line

The point-slope form of the equation of a line is given as

`\begin{gathered} y-y_1=m(x-x_1) \\ \text{where m=slope, (x}_1,y_1)\text{ is the point} \end{gathered}`

From the questions, the given point are

`\begin{gathered} x_1=-2,x_2=5 \\ y_1=3,y_2=-3 \end{gathered}`

The slope m, of the line is given by

`m=(y_2-y_1)/(x_2-x_1)`

Substituting the values given we have

`\begin{gathered} m=(-3-3)/(5-(-2))=(-6)/(7) \\ m=(-6)/(7) \end{gathered}`

Then the point-slope form for the equation of the line is

`y-3=-(6)/(7)(x-5)`