Question

What is the slope of the line passing through the following points: `(-1, -2), (4,-5)`?

Answer 1

Slope (gradient )`-> -3/5`

Explanation:

Slope (gradient) is the amount of up or down for the amount of along. Like the incline on a hill.

Always read from left to right. If you go up reading left to right then it is a positive gradient. If you go down reading left to right then it is a negative gradient.

Gradient`->("change in y-axis")/("change in x-axis")`

A memory jog could be "Why is this one on top".

Let Point 1`->P_1->(x_1,y_1)->(-1,-2)`

Let Point 2`->P_2->(x_2,y_2)->(4,-5)`

Let gradient be `m`

Gradient`color(white)(.)(m) ->("change in y-axis")/("change in x-axis")->(y_2 - y_1)/(x_2-x_1)`

`m=(-5-(-2))/(4-(-1)) = (-3)/5 = -3/5`

This is negative so for 5 along it goes down 3.