Question

How do you find the slope and intercept of `3x-2y=9`?

Answer 1

See a solution process below:

Explanation:

This equation is in Standard Linear Form. The standard form of a linear equation is: `color(red)(A)x + color(blue)(B)y = color(green)(C)`

Where, if at all possible, `color(red)(A)`, `color(blue)(B)`, and `color(green)(C)`are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

`color(red)(3)x + (color(blue)(-2))y = color(green)(9)`

The slope of an equation in standard form is: `m = -color(red)(A)/color(blue)(B)`

Substituting gives:

`m = -color(red)(3)/color(blue)(-2) = 3/2`

The `y`-intercept of an equation in standard form is: `color(green)(C)/color(blue)(B)`

Substituting gives:

`color(green)(9)/color(blue)(-2) = -9/2` or `(0, -9/2)`