Question

Which of the following are incorrect expressions for slope?

Answer 1

Choice B and choice C are incorrect expression for slope.

Explanation:

Slope is defined as the steepness of a line. It is also called gradient.It is denoted by m.

It is ratio of change in the dependent variable and independent variable.

hence, m = Δy / Δx = y₂-y₁ / x₂-x₁

The change in dependent variable is called rise and the change in dependent variable is called run.

So, m = rise / run

hence, choice B. and choice C. are incorrect expressions for slope.

Answer 2

Option B and C are correct.

`(x_2-x_1)/(y_2-y_1)`

`(run)/(rise)` are the expression incorrect for slope

Explanation:

Slope is defined as the change in the dependent variable relative to the change in the dependent variable

or the ratio of the horizontal changes to vertical changes between any two points on the graph of the line.

The vertical changes between any two points is rise

The horizontal changes between any two points is run.

Formula for slope is given by:

For any two points
`(x_1, y_1)` and
`(x_2, y_2)`

then slope is:

`\text{Slope} =(rise)/(run)= (y_2-y_1)/(x_2-x_1)`

or we can write this as:

Δy =
`y_2-y_1`

Δx =
`x_2-x_1`

⇒
`\text{Slope} = (\triangle y)/(\triangle x)`

Therefore, the expression which are incorrect for slope are;

`(x_2-x_1)/(y_2-y_1)`

`(run)/(rise)`