Question

How do you find the slope intercept form for x-intercept 3, y-intercept 2/3?

Answer 1

`y=(-2/9)x+(2/3).`

Explanation:

Eqn. of a line having its X & Y intercepts a,b, resp., is `x/a+y/b=1.`

In our case, it is `x/3+y/(2/3)=1`, i.e., `x/3+(3/2)y=1`, or, `2x+9y=6`.

Now to transform this in slope-intercept form [`y=mx+c`], we rearrange it as `9y=-2x+6`, or, `y=(-2/9)x+(6/9)`, i.e., `y=(-2/9)x+(2/3).`

Alternatively :-

We already know the Y-intercept of the line, `(2/3).`

So, we have to find its slope only.

Now, X-intercept is `3`, means the line passes thro. the pt. `(3,0).`
Similarly, from Y-intercept, we get another pt. `(0,2/3).`
Using these pts., we compute the slope of the line as `(2/3-0)/(0-3)=-2/9.`

With slope `m=-2/9` & Y-intercept `c=2/3`, the reqd. eqn. is `y=(-2/9)x+(2/3)`, as before!