1. Lines that have a positive slope ‘rise’ through the x-y plane.
Slopes of Lines
Slope = rise =
run
Lines that have a positive slope
‘rise’ through the x-y plane.
The greater the slope of a line,
the steeper the line will be.
( smallest slope – blue line
biggest slope – green line)

2. Slope-Intercept form: y = mx + b
Lines with negative slope
‘fall’ through the x-y plane
The greater the ‘absolute value’
Of the slope the steeper the
‘fall’ will be.
Slope-Intercept form: y = mx + b
m = slope; b = y-intercept
Therefore to quickly find the slope and y-intercept,
‘Dah’—Just solve the equation for y!

3. This information allows us to graph lines quickly and easily.
Example 1: Find the slope and y-intercept of
7x + 13y = 26
1st: Isolate the ‘y’ term: x x
13y = -7x + 26
2nd: Get ‘y’ all alone 
Voila  y = (-7/13)x + 2
Align y = m x + b
To see that m = -7/13
and that b = 2
Now Graph!

4. All non vertical lines are parallel - (ll) - if they have the
‘same slope’!
Slopes of perpendicular lines – ‘ l .’ – are
‘opposite reciprocal slopes’
Example 2: A line, ‘l’ has equation x + 2y = 5
What is the slope of the line: ??
(solve for y to find the ‘m’ value)
Parallel to ‘l’ b) Perpendicular to ‘l’
(To be (ll) the line must have
the same ‘m’ value) (Here the ‘m’ value must be the
opposite reciprocal)
m = -1/ m = 2/1 or 2

5. The graphs below illustrate the effects of ‘m’ and ‘b’
on an equation written in slope-intercept form. Guess
what is common about the lines in the two graphs.
What is common What is common
here? here?
same y-intercept same slope

6. Remember: Two lines are parallel if they have ???
And two lines are perpendicular if they have ???
Example 3: The equations of three lines are given.
Which lines are parallel (ll) and which lines are
perpendicular ( l .)?
(Solve each equation for y – then compare the ‘m’ vlaues)
y = (3/4)x – 7 b) 4x + 3y = 10 c) 6x – 8y = 11
Example 4: Find the value of ‘k’ if the line joining
(2,k) with (4,5) is:

7. now set k – 5 = - 1 (opposite reciprocal slope)
Parallel to y = 3x+1
(Using the points (2,k) and (4,5) ‘Calculate the slope: ??
k – 5
2 – 4
k – Now set this equal to 3
proportion: k – 5 = 3
cross multiply and solve for k.
k – 5 = - 6
k = - 1
Perpendicular to y = 3x+1
now set k – 5 = (opposite reciprocal slope)
Cross multiply and solve for ‘k’
3k – 15 = 2
3k = 17
k = 17 3