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

1 Answer
Ratnaker Mehta
Jun 14, 2016

#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!

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