Question

What is the equation of a line passing through the point (a, b) and having a slope of b?

Answer 1

The equation is y-a= b(x-b)

Explanation:

I use bold for the slope so you can differentiate the slope term b from the y coordinate value b.

The equation of a line passing through a specific point and having a specific slope can be obtained using the point slope form of a line :

y-y1=m(x-x1) where m is the slope and (x1,y1) is your specific point.

So replacing your values, the point (x1,y1) =(a,b) and m=b, in this equation we havE:

y-a= b(x-b)

That can be expressed in point slope form and explicit for as.

y = b(x-b) + a = bx -bb +a =

y= bx + (a -bb)

Answer 2

From the slope form of a line;

`(y-b)/(x-a) =b`
y-b=bx-ab
y=bx-ab+b
y=bx-b(a-1)