Question

Find the point slope form of the equation of the line passing through the points (-6,-4) and (2,-5)

Answer 1

`y+4=-(1)/(8) *(x+6)` or
`y+5=-(1)/(8) *(x-2)` is the slope point form of the line.

Explanation:

The given points are (-6,-4) and (2,-5) are as
`\left(x_(1), y_(1)\right) \text { and }\left(x_(2), y_(2)\right)`. Need to find out the point slope form of the line which passes through these points. The formula of slope point form for an equation of a straight line as

`\left(y-y_(1)\right)=\text { slope } *\left(x-x_(1)\right)`

Hence, we have two points and we have to find out first slope of the line

`\left(y-y_(1)\right)=m *\left(x-x_(1)\right)`

Where m is the slope and
`\left(x_(1), y_(1)\right)` is a point the line passes through. Hence, we have two points and we have to find out first slope of the line

`\text {slope}=(-5-(-4))/(2-(-6))=-(1)/(8)`

Now, slope point form of the line is,

`y-(-4)=-(1)/(8) *(x-(-6))`

`y+4=-(1)/(8) *(x+6)`

Similarly at (2,5),

`y-(-5)=-(1)/(8) *(x-2)`

`y+5=-(1)/(8) *(x-2)`