Question

How do you find a equation of the line containing the given pair of points (-5,0) and (0,9)?

Answer 1

I found: `9x-5y=-45`

Explanation:

I would try using the following relationship:

`color(red)((x-x_2)/(x_2-x_1)=(y-y_2)/(y_2-y_1))`

Where you use the coordinate of your points as:
`(x-0)/(0-(-5))=(y-9)/(9-0)`
rearranging:
`9x=5y-45`
Giving:
`9x-5y=-45`

Answer 2

`y=(9/5)*x+9`

Explanation:

You are searching the equation of a straight line (=linear equation) who contain `A(-5,0) and B(0,9)`

A linear equation form is : `y=a*x+b`, and here we will try to find numbers `a` and `b`

Find `a` :

The number `a` representing the slope of the line.

`a = (y_b-y_a)/(x_b-x_a) = Delta_y/Delta_x`

with `x_a` representing the abscissa of the point `A` and `y_a` is the ordinate of the point `A`.

Here, `a = (9-0)/(0-(-5)) = 9/5`

Now our equation is : `y=(9/5)*x+b`

Find `b` :

Take one point given, and replace `x` and `y` by the coordinate of this point and find `b`.

We are lucky to have one point with `0` in abscissa, it makes the resolution easier :

`y_b = (9/5)*x_b + b`
`9 = (9/5)*0 + b`
`b = 9`

Therefore, we have the equation line !

`y = (9/5)*x+9`