Question

How do you write the slope-intercept equation of a line with point (2,1) with slope -2/3?

Answer 1

`y=-2/3x+7/3`

Explanation:

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

`color(red)(|bar(ul(color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))`
where m represents the slope and b, the y-intercept.

Here we know m but have to find b.

`color(blue)"Partial equation"" is " y=-2/3x+b`

To calculate b, substitute x = 2 and y = 1 from (2 ,1) into the partial equation.

`rArr(-2/3xx2)+b=1rArr-4/3+b=1rArrb=7/3`

`rArry=-2/3x+7/3" is equation in slope-intercept form"`