Question

What is the slope of the line `-2x-5y=11`?

Answer 1

See a solution process below:

Explanation:

We can transform this line to the Standard Form for Linear Equations. 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

To transform this equation we need to multiply each side of the equation by `color(red)(-1)` to ensure the coefficient for `x` is positive while keeping the equation balanced:

`color(red)(-1)(-2x - 5y) = color(red)(-1) xx 11`

`(color(red)(-1) xx -2x) + (color(red)(-1) xx - 5y) = -11`

`color(red)(2)x + color(blue)(5)y = color(green)(-11)`

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

Substituting the `x` and `y` coefficients gives:

`m = -color(red)(2)/color(blue)(5)`

Answer 2

The slope is `-2/5`.

Explanation:

Find the slope:

`-2x-5y=11`

Solve for `y`, which will give you the slope intercept form of a linear equation: `y=mx+b`, where `m` is the slope and `b` is the y-intercept.

Add `2x` to both sides of the equation.

`-color(red)cancel(color(black)(2x))+color(red)cancel(color(black)(2x))-5y=2x+11`

Simplify.

`-5y=2x+11`

Divide both sides by `-5`.

`(color(red)cancel(color(black)(-5))y)/(color(red)cancel(color(black)(-5)))=-2/5x-11/5`

Slope intercept form.

`y=-2/5x-11`

The slope is `-2/5`