Question

How do you write an equation of a line with point (2,-2), slope `2/7`?

Answer 1

`y=2/7x-18/7`

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=2/7" and " (x_1,y_1)=(2,-2)`

substituting these values into the equation.

`y-(-2)=2/7(x-2)`

`rArry+2=2/7(x-2)larrcolor(red)" in point-slope form"`

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

`y+2=2/7x-4/7`

`rArry=2/7x-18/7larrcolor(red)" in slope-intercept form"`