we are given
[tex] ax+by=d [/tex]
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
[tex] y=mx+b [/tex]
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
[tex] ax+by-ax=d-ax [/tex]
[tex] by=-ax+d [/tex]
step-2: Divide both sides by b
[tex] \frac{by}{b} =\frac{-ax}{b} +\frac{d}{b} [/tex]
[tex] y =-\frac{a}{b}x +\frac{d}{b} [/tex]
now, we can compare this with slope intercept form of equation
[tex] y=mx+b [/tex]
and we get
[tex] m=-\frac{a}{b} [/tex]
[tex] b=\frac{d}{b} [/tex]...................Answer
