Question

How do you write a equation of a line through point (-6,4) and has a slope of -5/2?

Answer 1

`y=-5/2x-11`

Explanation:

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

`color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))`
where m represents the slope and `(x_1,y_1)" a point on the line"`

`"here "m=-5/2" and " (x_1,y_1)=(-6,4)`

`rArry-4=-5/2(x-(-6))`

`rArry-4=-5/2(x+6)larrcolor(red)" in point-slope form"`

distributing the bracket and simplifying gives an alternative version of the equation.

`y-4=-5/2x-15`

`rArry=-5/2x-15+4`

`rArry=-5/2x-11larrcolor(red)" in slope-intercept form"`