Question

How do you find the slope of the line passing through the points (1,6) and (10, -9)?

Answer 1

`"slope" = -15/9`

Explanation:

To find the slope, you need to use the following formula

`Slope = (Deltay)/(Deltax)->(y_2-y_1)/(x_2-x_1)`

Slope basically tells us a little about the line on our graph. How steep is it? Is it negative or positive? Is there a zero slope (horizontal line)?

You take whatever you are given and work with that to solve for the unknown. Here, we are given 2 points on a graph.

`color(white)(aaaaaaaaaaaa)(1, 6)`
`color(white)(aaaaaaaaaaaa)(10, -9)`

The first number corresponds to the point on the `"x axis"`. The second number corresponds to the point on the `"y axis"`. We can arbitrarily decide which is our `(x_1, y_1)` and which is our `(x_2, y_2)`

`color(white)(aaaaaaaaaaaaa)color(red)((1, 6)->(x_1, y_1))`
`color(white)(aaaaaaaaaaaaa)color(blue)((10, -9)->(x_2, y_2))`

`Slope = (Deltay)/(Deltax)->(y_2-y_1)/(x_2-x_1)->((color(blue)"-9"-color(red)"6"))/((color(blue)"10"-color(red)"1")) = color(orange)(-15/9)`

`Answer: "slope" = color(orange)(-15/9)`