Question

What is the slope intercept form of the line passing through `(2,3)` with a slope of `-3/2`?

Answer 1

`y = -3/2x + 6`

Explanation:

The slope-intercept form of a linear equation with two variables is :

`y = mx + c`

[ Where, `m` is the slope of the line,

and, `c` is the y-intercept].

So, We know the Slope, So, Just substitute `m` with the value of `-3/2`.

So, The equation now becomes :-

`y = -3/2x + c`

But, We have another thing to take care of.

We are given that the line must pass through `(2, 3)`.

So, The Values `2` and `3` must satisfy the equation.

So, The equation now becomes :-

`color(white)(xxx)3 = -3/cancel2 xx cancel2 + c`

`rArr c - 3 = 3`

`rArr c = 6`

So, Got the Y-Intercept.

So, The Finalised Equation now is :-

`y = -3/2x + 6`

Hope this helps.