Question

A line passes through the given points. Write an equation for the line in

point-slope form. Then rewrite the equation in slope-intercept form.
(4, -2), (9, -8)

Answer 1

4-9=5

-2--8=6

y=mx+b

slope/mx=6/1

base/y intercept=5

Answer 2

Answer: The equation for the line in point-slope form :
`(y+2)=(-6)/(5)(x-4)`

The equation in slope-intercept form :
`y=(-6)/(5)x+(14)/(5)`

Explanation:

The equation of a line in point slope form passing through points (a,b) and (c,d) is given by :-

`(y-b)=(d-b)/(c-a)(x-a)`

Now, the point slope form passing through points (4, -2) and (9, -8) is given by :-

`(y-(-2))=(-8-(-2))/(9-4)(x-4)\\\\\Rightarrow (y+2)=(-6)/(5)(x-4)`

The equation for the line in point-slope form :
`(y+2)=(-6)/(5)(x-4)`

Further if we simplify the equation , we get

`y+2=(-6)/(5)x+(24)/(5)\\\\\Rightarrow\ y=(-6)/(5)x+(24)/(5)-2\\\\\Rightarrow\ y=(-6)/(5)x+(14)/(5)`

The equation in slope-intercept form :
`y=(-6)/(5)x+(14)/(5)`