Question

What is the equation of the line with slope `m= -11/3` that passes through `(13/15,-23/24)`?

Answer 1

`y=-11/3x+799/360`

Explanation:

Recall that the general equation of a line is:

`color(blue)(|bar(ul(color(white)(a/a)y=mx+bcolor(white)(a/a)|)))`

where:
`y=`y-coordinate
`m=`slope
`x=`x-coordinate
`b=`y-intercept

Determining the Equation
`1`. Start by substituting `color(orange)(m=-11/3)` into the formula.

`y=mx+b`

`y=color(orange)(-11/3)x+b`

`2`. Since you are also given the coordinate, `(color(purple)(13/15),color(teal)(-23/24))`, substitute it into the equation as well.

`color(teal)(-23/24)=color(orange)(-11/3)color(purple)((13/15))+b`

`3`. Solve for the unknown value of the variable, `b`.

`-23/24=-143/45+b`

`b=799/360`

`4`. Rewrite the equation.

`color(green)(|bar(ul(color(white)(a/a)y=-11/3x+799/360color(white)(a/a)|)))`