Question

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

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 :$(y+2)=\dfrac{-6}{5}(x-4)$

The equation in slope-intercept form : $y=\dfrac{-6}{5}x+\dfrac{14}{5}$

Step-by-step explanation:

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

$(y-b)=\dfrac{d-b}{c-a}(x-a)$

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

$(y-(-2))=\dfrac{-8-(-2)}{9-4}(x-4)\\\\\Rightarrow (y+2)=\dfrac{-6}{5}(x-4)$

The equation for the line in  point-slope form :$(y+2)=\dfrac{-6}{5}(x-4)$

Further if we simplify the equation , we get

$y+2=\dfrac{-6}{5}x+\dfrac{24}{5}\\\\\Rightarrow\ y=\dfrac{-6}{5}x+\dfrac{24}{5}-2\\\\\Rightarrow\ y=\dfrac{-6}{5}x+\dfrac{14}{5}$

The equation in slope-intercept form : $y=\dfrac{-6}{5}x+\dfrac{14}{5}$