I’m a little foggy – what is the slope of a line?

Slope refers to the steepness of a line.

Slope is described asriserun .

The formula for slope is:y2 - y1

x2 - x1

This formula is used to find the slope of a line throughthe points (x1, y1) and (x2, y2).

Colored note card:

Slope

• steepness of a line

• described asriserun

• formula for slope is:y2 - y1

x2 - x1

Horizontal line – slope = 0

Vertical line – slope is undefined

Positive slope -

Negative slope -

White note card

Parallel and Perpendicular lines

Parallel lines-coplanar-never intersect-symbol - //

Perpendicular lines-coplanar-intersect to form 90° angles-symbol -

Skew lines-noncoplanar-never intersect

So, what about the slopes of parallel and perpendicular

lines?

The slopes of parallel lines are equal!

And the slopes of perpendicularlines are opposite reciprocals (theirproduct is -1)!

For perpendicularlines I just flip the slope and change to its opposite.That’s what I said!

Colored note card:

Slopes of // and lines

• slopes of parallel lines are the same

• slopes of perpendicular lines are opposite reciprocals (flipped and made opposites)

Example: slope = ½

Slope of parallel line:

Slope of perpendicular line:

½

-2/1 or -2

Find the slope of a line parallel and a line perpendicular to the given line.

• the line through (-5, 2) with a slope of ¾

• y = -3x + 4

• the line through (-2, 6) and (4, -1)

The fog is clearing! Just to review: parallel lines never intersect and perpendicular lines intersect to form right

angles. The slopes of parallel lines are equal.

The slopes of perpendicular lines have a product of -1 -

or they are opposite reciprocals. I think I’ve got

it!

1. All five of the lines below are to be graphed on the same coordinate graph. Without graphing, describe how the graphs of the lines are related (parallel, perpendicular,

intersecting). Justify your answers (you could set up your answer as a two column table).

Line a - y = -5/2 x + 6Line b - through (1, -4) with slope 2/5Line c - through (7, 10) and (13, -5)Line d - y = 2x - 15Line e - through (5, 8) and (15, 12)

2. Graph each of the lines from #1 on the same coordinate graph. Label each line. Were the relationships you described in #1 correct?

Line a - y = -5/2 x + 6Line b - through (1, -4) with slope 2/5Line c - through (7, 10) and (13, -5)Line d - y = 2x - 15Line e - through (5, 8) and (15, 12)

3. Write the equation of a line that is perpendicular to line e.Write the equation of a line that is parallel to line e.