2.2 Lines, 2.3 Lines, Slope

Calculating Slope

Given two points on the line   ( x_1, y_1) and   ( x_2, y_2), you can calculate the slope of a line by the following formula.

  m= {y_2-y_1} / {x_2-x_1}

  y_2-y_1 is also know as   Delta y or “the change in y.”

  x_2-x_1 is also know as   Delta x or “the change in x.”

 

  m= {y_2-y_1} / {x_2-x_1} ={Delta y} /{Delta x} ={rise}/{run} 

Example: Calculate the slope of the line containing the points   ( 5, 7) and   ( 9, 10).

Solution: Choose one of the points to be   ( x_1, y_1) and choose the other point to be   ( x_2, y_2).

I will choose   ( 5, 7)  to be   ( x_1, y_1)  and choose   ( 9, 10) to be   ( x_2, y_2).

Substitute these values into the slope formula and simplify.

  m= {y_2-y_1} / {x_2-x_1} ={10-7}/{9-5} =3/4

The slope of the line containing the points   ( 5, 7) and   ( 9, 10)  is m= 3/4.

Example: Calculate the slope of the line containing the points   ( -7, -2) and   ( 8, 8).

Solution: Choose one of the points to be   ( x_1, y_1) and choose the other point to be   ( x_2, y_2).

I will choose   ( -7, -2)  to be   ( x_1, y_1)  and choose   ( 8, 8) to be   ( x_2, y_2).

Substitute these values into the slope formula and simplify.

  m= {y_2-y_1} / {x_2-x_1} ={8-(-2)}/{8-(-7)}={8+2}/{8+7} =10/15=2/3

The slope of the line containing the points   ( -7, -2) and   ( 8, 8)  is m= 2/3.

Example: Finding the slope with the formula.

Example: Finding the slope with the formula.

Example: Finding the slope from the graph.