Question

What is the point slop form and the points on these?

Answer 1

Point slope form of a line:

`\begin{gathered} y-y_1=m(x-x_1) \\ \\ m:slope \\ (x_1,y_1):point \end{gathered}`

_________

First line:

Use the next formula to find the slope:

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

Points: (-2,3) and (8,-5)

`m=(-5-3)/(8-(-2))=(-8)/(10)=-(4)/(5)`

Use one of the points and the slope to write the equation in point-slope form:

`\begin{gathered} y-3=-(4)/(5)(x-(-2)) \\ \\ y-3=-(4)/(5)(x+2) \end{gathered}`Point slope form: y-3=-4/5(x+2)Point (-2,3)

_____________________

Second line:

Points: (-1,-6) and (0,-2)

`m=(-2-(-6))/(0-(-1))=(-2+6)/(0+1)=(4)/(1)=4`

Use one of the points and the slope to write the equation in point-slope form:

`\begin{gathered} y-(-6)=4(x-(-1)) \\ \\ y+6=4(x+1) \end{gathered}`Point slope form: y+6=4(x+1)Point: (-1,-6)