Question

How do you find the slope of this equation: x/3 + y/4=1?

Answer 1

See the solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(12)` to put the equation in Standard Form for a linear equation. 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)(12)(x/3 + y/4) = color(red)(12) * 1`

`(color(red)(12) * x/3) + (color(red)(12) * y/4) = 12`

`color(red)(4)x + color(blue)(3)y = color(green)(12)`

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

Substituting for `color(red)(A)` and `color(blue)(B)` gives:

`m = -color(red)(4)/color(blue)(3)`