Numbers, Relations & Functions 10 Section 6.1

Numbers, Relations & Functions 10 Section 6.1

Slope of a Line

The slope of a line segment on a coordinate grid is the measure of its rate of change:

Example 1: Determining the Slope of a Line Segment

Determine the slope of the line segment shown.

Solution:

When a line segment goes up to the right, both y and x increase.

Both the rise and run are positive, so the slope of the line segment is positive.

When a line segment goes down to the right, y decreases and x increases. The rise is negative and the run is positive, so the slope of the line segment is negative.

For a horizontal line segment, the rise is zero, For a vertical line segment, the run is zero,

so the slope of the line segment is zero. so the slope of the line segment is undefined.

Example 2: Drawing a Line Segment with a Given Slope

Draw a line segment with each given slope.

a.  slope = b. slope =

Solution:

a.  A line segment with slope has a rise of _____ and a run of _____. Start at any point on the grid and move _____ units ______and _____ units ______.

b.  A line segment with slope can be written as _____ and has a rise of _____ and a run of _____. Start at any point on the grid and move _____ units ______and _____ unit ______.

Example 3: Determining Slope Given Two Points on a Line

Determine the slope of the line that passes through A(–5, –4) and B(3, 1)

Solution:

Example 4: Interpreting the Slope of a Line

Tom has a part-time job. He recorded the hours he worked and his pay for 3 different days. Tom plotted these data on a grid.

a.  What is the slope of the line through these points?

b.  What does the slope represent?

Solution: