Question

Find an equation for the line below.

Answer 1

`y - 6=(1)/(3)(x - 4)`

OR

`y=(1)/(3)x + 4(2)/(3)`

Explanation:

We can write the equation for the graphed line in point-slope form:

• 
  `y - b=m(x - a)`

where
`m` is the line's slope and
`(a,b)` is a point on the line.

First, we can find
`m`, the line's slope, using the formula:

`m = \frac{\text{rise}}{\text{run}} = (\Delta y)/(\Delta x)`

(Remember that
`y` is the vertical axis, and
`x` is the horizontal one.)

`m = (2)/(6)`

`m=(1)/(3)`

Next, we can identify a point on the line as:

• 
  `(4,6)`

so we can assign the variable values:

• 
  `a=4`
• 
  `b=6`

Finally, we can piece together the point-slope form equation of the line:

`y - b=m(x - a)`

↓ plugging in the variable values

`\boxed{y - 6=(1)/(3)(x - 4)}`

___

If necessary, we can also solve for y to put this into slope-intercept form:

`y=(1)/(3)(x - 4) + 6`

`y=(1)/(3)x - (4)/(3) + 6`

`y=(1)/(3)x + 4(2)/(3)` OR
`y=(1)/(3)x + (14)/(3)`