Question

What is the equation of the line passing through `(24,18)` and `(9,12)`?

Answer 1

`y=2/5x+42/5`

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"`

`"to calculate m use the "color(blue)"gradient formula"`

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

`"let "(x_1,y_1)=(24,18)" and "(x_2,y_2)=(9,12)`

`m=(12-18)/(9-24)=(-6)/(-15)=2/5`

`y=2/5x+blarrcolor(blue)"is the partial equation"`

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

`"using "(9,12)" then"`

`12=18/5+brArrb=60/5-18/5=42/5`

`y=2/5x+42/5larrcolor(red)"is equation of line"`

Answer 2

`y=2/5*x+42/5`

Explanation:

We get the slope as
`m=(y_2-y_1)/(x_2-x_1)=(12-18)/(9-24)=2/5`
so we have
`y=2/5x+n`
using
`x=9,y=12`
we get
`n=42/5`