Question

The graph of a line passes through the points (0, -2) and (6.0). What is

the equation of the line?

Answer 1

`y=(1)/(3)x-2`

Explanation:

The equation of a line is given in the form
`y=mx+b`

Where

m is the slope with formula
`m=(y_2-y_1)/(x_2-x_1)`

and

b is the y-intercept [y axis cutting point of line]

Given the two points (0, -2) and (6,0),

x_1 = 0

y_1 = -2

x_2 = 6

y_2 = 0

Now, we find m using formula:

`m=(0+2)/(6-0)=(1)/(3)`

Now we have

`y=(1)/(3)x+b`

Finding b, we plug in any (x,y) point. Lets put (6,0) and find b:

`y=(1)/(3)x+b\\0=(1)/(3)(6)+b\\0=2+b\\b=-2`

Thus,

equation of line =
`y=(1)/(3)x-2`