Question

Robert says that the slope of a line passing through (1, 7) and (3, 9) is equal to the ratio 1-3/7-9 . Is this a correct method for calculating the slope? Explain your answer. (1 point)

Answer 1

The slope should be calculated using the formula
`(7 - 9) / (1 - 3)` instead of the one that was proposed in the question.

Explanation:

The slope of a line in a cartesian plane is the rate at which
`y` changes with respect to
`x`.

For this line, the value of
`y` increased (vertically) from
`7` at
`(1,\, 7)` to
`9` at
`(3,\, 9)` as the value of
`x` increased (horizontally) from
`1` to
`3`.

In other words,
`y` changed by
`(9 - 7)` while
`x` changed by
`(3 - 1)`.

The slope of the line (rate at which
`y` changes with respect to
`x`) would be:

`\displaystyle \frac{\text{rise}}{\text{run}} = ((9 - 7))/((3 - 1)) = ((7 - 9))/((1 - 3))`.

In general, for a line that goes through
`(x_1,\, y_1)` and
`(x_2,\, y_2)`, where
`x_(1) \\e x_(2)`:

`\begin{aligned}\text{slope}&= ((y_1 - y_2))/((x_1 - x_2)) = ((y_2 - y_1))/((x_2 - x_1))\end{aligned}`.