Question

How do you find the slope for \[\left( {4, - 4} \right)\& \left( { - 6, - 5} \right)\] ?

Answer 1

Hint: We will find the slope using the formula of the slope. We will consider the points as A and B with assigning the coordinates of the points. This can be a segment or two points on the line.

Formula used:Slope \[m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\]

Complete step-by-step solution:
Let, \[A = \left( {{x_1},{y_1}} \right) = \left( {4, - 4} \right)\& B = \left( {{x_2},{y_2}} \right) = \left( { - 6, - 5} \right)\]
Formula of the slope is given by,
   \[m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\]
Substituting the values,
\[m = \dfrac{{ - 5 - \left( { - 4} \right)}}{{ - 6 - 4}}\]
On calculating we get,
\[m = \dfrac{{ - 5 + 4}}{{ - 10}}\]
\[m = \dfrac{{ - 1}}{{ - 10}}\]
Cancelling minus sign,
\[m = \dfrac{1}{{10}}\]
This is the slope of the given line or segment.

Therefore \[m = \dfrac{1}{{10}}\].

Note: Note that slope is the ratio of the difference in the y coordinates and x coordinates. Slope of a line indicates whether the line is increasing or decreasing. If the slope is positive then the line is increasing and if the slope is negative then the line is decreasing. Slope intercept form of a line is \[y = mx + c\] where m is the slope and intercepts are x and y intercepts.