Question

What is the equation of the line with slope `m= -5` that passes through `(-13,-7)`?

Answer 1

`y=-5x-72`

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"`

`"here "m=-5`

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

`"to find b substitute "(-13,-7)" into "`
`"the partial equation"`

`-7=65+brArrb=-7-65=-72`

`y=-5x-72larrcolor(red)"is the equation of line"`

Answer 2

`y=-5x+b`

Explanation:

Equation of line in slope format is `y=mx+b`, where `m` is the slope of the line and `b` is y-intercept.

Hence from the given data, the equation of the line is:

`y=-5x+b`

Now, we can calculate the value of `b` from points `(-13,-7)`.

`y=-5x+b`

`-7 = -5(-13) +b`

`-7 = 65+b`

`-7-65=b`

`b=-72`

Therefore equation of line in slope format is `y=-5x+b`