Question

What is the equation of the line between `(12,7)` and `(9,14)`?

Answer 1

`7x+3y-105=0`

Explanation:

The equation of the line passing through the points `(x_1, y_1)\equiv(12, 7)` & `(x_2, y_2)\equiv(9, 14)` is given by following formula

`y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)`

`y-7=\frac{14-7}{9-12}(x-12)`

`y-7=-\frac{7}{3}(x-12)`

`3y-21=-7x+84`

`7x+3y-21-84=0`

`7x+3y-105=0`

Answer 2

`y=-7/3x+35`

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"`

`"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)=(12,7)" and "(x_2,y_2)=(9,14)`

`m=(14-7)/(9-12)=7/(-3)=-7/3`

`y=-7/3x+clarrcolor(blue)"is the partial equation"`

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

`"using "(12,7)" then"`

`7=-28+crArrc=7+28=35`

`y=-7/3x+35larrcolor(blue)"equation in slope-intercept form"`