4.4  The Slope of a Line

Mrs. Agriesti's Algebra

Goal:  To use two points on a line to find the slope of the line.

Slope -  The value that describes the slant of a line.
y₂ -  Is read "y sub 2" and means "y from the second point".

Slope Formula:

y₂  is the y-value from the second point.
y₁ is the y-value from the first point.
x₂  is the x-value from the second point.
x₁ is the x-value from the first point.

Looking at the line left to right, like you read:

• The slope is positive if the line goes up.
  
• The slope is negative if the line goes down.
  
• The slope is 0 (zero) if the line is horizontal.
  

• There is no slope (it is undefined) if the line is vertical. 
  

Zero slope has no rise but it does have run (0/x), no slope has rise but no run (x/0 - which is undefined because you can't divide by zero).

Estimate the slope of each line:

First locate two places where the line crosses the grid intersections (grid corners).

I see three for this line:  (0,4), (3,2), & (6,0).

Plug the x and y values from two of those points into the formula and solve.  Be careful with the signs.

It doesn't matter which two points you use.  Using the last two points gives you the same answer.

First locate two places where the line crosses the grid intersections (grid corners).

I see five for this line:  (-4,-3), (-3,-1), (-2,1), (-1, 3), & (0,5).

Plug the x and y values from two of the points into the formula and solve.  Be careful with the signs.

Using any two of the points results in the same answer.