Question

What is the slope of the line through the points (-2, -5) and (1, -7)?

Answer 1

Reqd. Slope `=(-5+7)/(-2-1)=2/-3=-2/3.`

Explanation:

Reqd. Slope `=(-5+7)/(-2-1)=2/-3=-2/3.`

Answer 2

Gradient is`" "-2/3`

Explanation:

The slope (gradient) is the amount of change in the up or down as we read from left to right for the given amount of along. This is rather like the slope (gradient) on a hill.

Let the left most point be `" "P_1->(x_,y_1) = (-2,-5)`
Let the right most point be `color(white)(.)P_2->(x_2,y_2)=(1,-7)`

Change in up or down is change in y `->(y_2-y_1)`

Change in along is change in x`" "->(x_2-x_2)`

`" Gradient "->("change in y")/("change in x")->(y_2-y_1)/(x_2-x_1)`

`" "(y_2-y_1)/(x_2-x_1)->(-7-(-5))/(1-(-2)) = (-7+5)/(1+2)`

`" gradient "=(-2)/(3) = -2/3`