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Pre-Algebra
Chapter 8
Sections 4 & 5 Quiz
How to find the slope of the line
• Remember – the slope is rise
run
So – to find the slope you subtract the rise
numbers of the ordered pair: the y axis
numbers. The answer is the rise. Then you
subtract the run numbers of the ordered pair:
the x axis numbers. The answer is the run.
Find the slope of a line
• For example if the questions asks: find the
slope of the lines:
• And you are given a graph that shows the
ordered pairs as (0,5) and (-1, 7).
• You first subtract 5 – 7 = 2. The RISE is 2
• Subtract 0 - -1 = remember that two negative
signs right together become a positive so you
have 0 + 1 = 1. The RUN is 1
Find the slope of a line
• So the slope of the line = 2/1
Negative/Positive/Zero/Undefined
• If the questions asks you to determine if the
line is negative/positive/zero/or undefined:
• First find the slope of the line (see previous
slides)
• Then determine which way the line would go
if you were to graph the line. If it is going
uphill the line is POSITIVE.
• If the line is going downhill, the line is
NEGATIVE.
Positive/Negative/Zero/Undefined
• If the rise = 0 that means the line is straight
across. There is NO RISE so the slope is ZERO.
• If the RUN is 0 that means the line will go
straight up and down – there will be no
movement horizontally. This line is
UNDEFINED.
Slope and Y-Intercept
• This equation is in slope intercept form:
Y = 2x + 3
This equation IS NOT in slope intercept form:
2x + y = 3
If an equation IS NOT in slope intercept form
then you will need to put it in slope intercept
form. To do this you must move the y to one
side of the = by itself – it cannot have another
number with it.
Slope and Y-Intercept
• So … in the case of the equation:
2x + y = 3
First – I move the 2x to the other side of the =
sign by doing the opposite function. 2x is
positive so I’m going to SUBTRACT 2x from it:
2x – 2x + y = 3 – 2x
Now I have
y = 3 – 2x
Slope Intercept Form
• Now,
y = 3 – 2x is in slope intercept
form which means:
• The y-intercept is 3. In slope intercept form
the y-intercept IS ALWAYS the constant (the
number without a variable).
• The slope is -2. In slope-intercept form the
slope IS ALWAYS the number with the variable.
Slope-Intercept Form
If the equation looks like this:
2y + 3x = 10
It IS NOT in slope-intercept form because the y is
on the same side as 3x AND it has a coefficient–
the 2. First, I have to put the equation in slope
intercept form.
SLOPE-INTERCEPT FORM
2y + 3x = 10
First – move the 3x to the other side. Do this by
subtracting 3x from BOTH sides:
2y + 3x – 3x = 10 – 3x
I now have: 2y = 10 – 3x
The equation is NOT in slope intercept form yet.
The y still has a 2 with it.
Slope-Intercept Form
2y = 10 – 3x
Now to get rid of the 2 and since the way it is
written tells me it is a multiplication problem I
do the opposite of that – which is division and
divide all terms by 2:
2y = 10 – 3x
2y 2 2
Slope-Intercept Form
I now have: y = 5 – 3x
2
The y-intercept is 5 and the slope is -3x
2
Parallel and Perpendicular Lines
The slope we are using is -2/1. In this equation the
y-intercept was 3.
• So, graph the 3
• Then you use the
slope to find the next
Place on the graph. The slope -2/1. This means
you would go DOWN from the star two points and
OVER 1 point. The line is going DOWNHILL which
means there is a negative slope.
Parallel and Perpendicular line
I have made a graph of the slope -2/1
I know the line is negative because it goes downhill.
Now, I need the slope of the parallel line. Since a
parallel line runs right along side the other line
(that’s what parallel means), the slope of the
PARALLEL line is the same as the original line: -2/1.
To find the slope of the PERPENDICULAR line (which
is defined as an intersecting line) the slope is the
opposite sign and the invert of the slope: +1/2.
QUESTIONS
• If you have any questions email me at:
• [email protected]