find the equation of a line passing through (6,9) and (0,0)

Answer 1

slope = (9-0)/(6-0) = 9/6 = 3/2 = 0

It goes through the origin, so y intercept = 0

in slope intercept form the equation is y=mx + b

y=(3/2)x + 0

y=3x/2 or

2y = 3x is the equation of the line through the two given points

check it by plugging in each point

2(0) = 3(0)

0 = 0

and

2(9) = 3(6)

18 = 18

Answer 2

First find the slope = rise/run = y₂ - y₁/x₂ - x₁ 

m = (0 - 9)/(0 - 6) = -9/-6 = 3/2

Now we can substitute in the slope and either point to find b the y-intercept

y = mx + b

0 = 3/2(0) + b

0 = 0 + b

0 = b

The equation is y = 3/2x