Question

How do you write an equation of a line with slope of 3 and contains the point (4, 9)?

Answer 1

`y=3x-3`

Explanation:

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`"here "m=3`

`rArry=3x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(4,9)" into the partial equation"`

`9=12+brArrb=9-12=-3`

`rArry=3x-3larrcolor(red)"is the equation of the line"`

Answer 2

`y = 3x-3`

Explanation:

You can use the equation of a line in point-slope form:
`y-y_{1} = m(x-x_{1})`

Make the following substitutions:
`x_{1} = 4` (the x-coordinate of the point)
`y_{1} = 9` (the y-coordinate of the same point)
`m = 3` (the slope of the line)

That will give you:
`y-9 = 3(x-4)`

Then simplify:
`y-9 = 3(x-4)`
`y-9 = 3x-12`
`y = 3x-3`