Question

How do you write the equation of the line that passes through the points (3, 6) and (5, 18) using function notation?

Answer 1

`f(x)=6x-12`

Explanation:

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

`•color(white)(x)y=mx+c`

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

`"calculate m using the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(3,6)" and "(x_2,y_2)=(5,18)`

`m=(18-6)/(5-3)=12/2=6`

`y=6x+clarrcolor(blue)"is the partial equation"`

`"to find c substitute either of the 2 given points into"`
`"the partial equation"`

`"using "(3,6)" then"`

`6=18+crArrc=6-18=-12`

`y=6x-12" or "f(x)=6x-12`

Answer 2

`y=6x-12`

Explanation:

After using formula equation of line passes through 2 points,

`(y-6)/(x-3)=(18-6)/(5-3)`

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

`y-6=6*(x-3)`

`y-6=6x-18`

`y=6x-12`