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

2 Answers
Jul 9, 2015

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

Jul 9, 2015

y=(9/5)*x+9enter image source here

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