Question

What is the slope of a line that passes through (-2, -3) and (1, 1)?

Answer 1

See a solution process below:

Explanation:

The formula for find the slope of a line is:

`m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `(color(blue)(x_1), color(blue)(y_1))` and `(color(red)(x_2), color(red)(y_2))` are two points on the line.

Substituting the values from the points in the problem gives:

`m = (color(red)(1) - color(blue)(-3))/(color(red)(1) - color(blue)(-2)) = (color(red)(1) + color(blue)(3))/(color(red)(1) + color(blue)(2)) = 4/3`

Answer 2

Slope: `4/3`

Explanation:

The slope of a line between two points `color(blue)(""(x_1,y_1))` and `color(green)(""(x_2,y_2))`
is the difference between the `y` coordinate values divided by the difference between the `x` coordinate values (taken in the same order);
that is
`color(white)("XXX")"slope" = (color(green)(y_2)-color(blue)(y_1))/(color(green)(x_2)-color(blue)(x_1))`

In this case we have the points `color(blue)(""(-2,-3))` and `color(green)(""(1,1))` (notice that the order of listing these does not matter)
So
`color(white)("XXX")"slope"=(color(green)1-color(blue)(""(-3)))/(color(green)1-color(blue)(""(-2)))=4/3`