Question

Write the rule ax+by=d in gradient-intercept form. Then state the gradient m and the y-intercept.

Answer 1

we are given

`ax+by=d`

To find gradient(m) and y-intercept(b) , we need to change this equation into slope intercept form of equation

slope intercept form of equation is

`y=mx+b`

where

gradient is m

y-intercept is b

now, we can change our equation into this form

For that , we will have to isolate y on left side

step-1: Move x terms on right side

`ax+by-ax=d-ax`

`by=-ax+d`

step-2: Divide both sides by b

`(by)/(b) =(-ax)/(b) +(d)/(b)`

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

now, we can compare this with slope intercept form of equation

`y=mx+b`

and we get

`m=-(a)/(b)`

`b=(d)/(b)`...................Answer