Question

What is the equation of a line that passes through `(2, —7)`, and has a slope of `3`?

Answer 1

`y=3x-13`

Explanation:

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

`•color(white)(x)y=mx+b`

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

`"here "m=3`

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

`"to find b substitute "(2,-7)" into the partial equation"`

`-7=6+brArrb=-7-6=-13`

`rArry=3x-13larrcolor(red)"is the equation of line"`

Answer 2

`color(indigo)(3x - y = 13)`

Explanation:

Point: `(x_1,y_1) = (2, -7)`

Slope `= m = 3`

The point - slope form equation is

`(y- y_1) = m *(x-x_1)`

So

`y + 7 = 3 * (x - 2)`

`y + 7 = 3x - 6`

`color(indigo)(3x - y = 7 + 6 = 13)`