Question

What is the equation of the line that passes through `(1,5)` and `(-2,14)` in slope intercept form?

Answer 1

`y=-3x+8`

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 the slope m use the "color(blue)"gradient formula"`

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

`"let "(x_1,y_1)=(1,5)" and "(x_2,y_2)=(-2,14)`

`rArrm=(14-5)/(-2-1)=9/(-3)=-3`

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

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

`"using "(1,5)" then"`

`5=-3+brArrb=5+3=8`

`rArry=-3x+8larrcolor(red)"in slope-intercept form"`

Answer 2

The reqd. equn. of the line is

`3x+y=8` or `y=-3x+8`

Explanation:

If `A(x_1,y_1) and B(x_2,y_2)`,then equation of the line:

`color(red)((x-x_1)/(x_2-x_1)=(y-y_1)/(y_2-y_1)`.

We have,

`A(1,5) and B(-2,14)`

So,

`(x-1)/(-2-1)=(y-5)/(14-5)`.

`=>(x-1)/-3=(y-5)/9`

`=>9x-9=-3y+15`

`=>9x+3y=15+9`

`=>9x+3y=24`

`=>3x+y=8` or `y=-3x+8`
graph{3x+y=8 [-20, 20, -10, 10]}