Question

How do you write the equation of a line given m= -5 (2,4)?

Answer 1

`y=-5x+14`

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 "(2,4)" into the partial equation"`

`4=-10+brArrb=4+10=14`

`y=-5x+14larrcolor(red)"is the equation of the line"`

Answer 2

See below:

Explanation:

As an alternate way of solving this, we can use the point slope form, which is:

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

Substituting in:

`color(blue)(ul(bar(abs(color(black)((y-4)=-5(x-2)))))`

We can convert this form into the slope intercept form shown in the other answer:

`y-4=-5x+10=>color(blue)(ul(bar(abs(color(black)(y=-5x+14`

And also into standard form:

`color(blue)(ul(bar(abs(color(black)(5x+y=14`

These all describe the same thing - this line:

graph{-5x+14[-20,20,0,20]}