Question

What is the equation in point-slope form and slope intercept form for the line given (-6,-4) AND (2,-5)?

Answer 1

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

Explanation:

For the given points `(x_1,y_1)=(-6,-4)` and `(x_2,y_2)=(2,-5)`

the slope can be determined as `m=(y_2-y_1)/(x_2-x_1)=(-5-(-4))/(2-(-6))=-1/8`

Using a general variable point `(x,y)` and `(x_1,y_1)` (as above)
we have the slope `m=(y-(-4))/(x-(-6))=(y+4)/(x+6)`

Since the slope is constant for all points on a straight line
`color(white)("XXX")(y+4)/(x+6)=-1/8`

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

Which is the slope-point form with
`color(white)("XXX")`slope `=(-1/8)`
and
`color(white)("XXX")` the point: `(-6,-4)`