SLOPE-INTERCEPT FORM
Linear Equations
What is Slope-Intercept Form?
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Slope-Intercept form is a way a line can be written.
It includes the slope and the y-intercept.
The equation is y=mx + b,
where m = the slope and b = the y-intercept
An Example of Slope-Intercept
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When given y=2/3x – 2, graph the linear
equation.
First, what is the y-intercept?
The y-intercept is -2!
Then, find the slope……
The slope is 2/3. What does that mean?
From each point, the line will rise up 2 and go right
3.
How do I Graph with Slope-Intercept?
The equation was y=2/3x – 2.
1st – Find the y-intercept….
-2, and place it on the
graph
2nd – Find the slope…..
The slope is 2/3.
Rise/Run so the graph
rises up 2 and runs 3.
3rd – Plot another point by
following the slope. The
next point will be at
(3, 0).
4th – Connect the two with a
line.
How Do I Write an Equation in SlopeIntercept Form When Given a Graph?
You need two things:
SLOPE AND Y-INTERCEPT
1st – Find the y-intercept.
Where does the line cross the y-axis?
The y-intercept is 4!
2nd – Is it a positive or negative slope?
Does it go up or down from left to right?
It goes down so it’s NEGATIVE!
3rd – Find another point where the line
crosses a grid intersection.
There is one at (1, 1)!
So, if slope is -3 and the yintercept is 4, what is the
equation?......
4th – Count the rise/run from the yintercept to the second point.
The line went down 3 and right 1.
So the slope is -3/1 which is -3.
y = -3x + 4
STANDARD FORM
Linear Equations
What is Standard Form?
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Standard form is another way to write a linear
equation.
The equation is …. ax + by = c
A and B are coefficients for the variables.
C is a number.
How Can I Graph from Standard Form?
You only need two points to draw a line.
Standard Form gives you the two
points…..the x and y intercepts!
3x - 6y = 12
1st – Find the x-intercept.
Make y = 0
3x - 6(0) = 12
3x - 0 = 12
3x = 12 so……
x intercept is 4!!!
2nd – Find the y-intercept.
Make x = 0
3(0) - 6y = 12
0 - 6y = 12
-6y = 12 so……
y = -2
Connect the dots by
drawing a straight
line. You have now
graphed your line.
How Can I Write Slope-Intercept Equations
in Standard Form?
When given y = 3x – 2, write the equation in
standard form
 Remember, Standard Form is ax + by = c.
 Follow these easy steps:
 y = 3x – 2
-3x -3x (subtract 3x from each side)
-3x + y = -2 or if you change the signs……
3x – y = 2…..either answer is acceptable.
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Let’s Try Some More
Write the following in Standard Form:
 y = 6x + 7
 y = 3x – 4
 y = -3x + 1
 y = 4x
 Answers:
 y = 6x + 7  -6x + y = 7 or 6x – y = -7
 y = 3x – 4  -3x + y = -4 or 3x – y = 4
 y = -3x + 1  3x + y = 1
 y = 4x  -4x + y = 0 or 4x – y = 0
WHAT ABOUT FRACTIONS???
y = -¾ x + 4
+ ¾x +¾x ( add ¾x to both sides)
¾x + y = 4 (There’s an ugly fraction there…ugh!)
How do you get rid of a FRACTION????
Multiply by the denominator.... Multiply EVERYTHING!!
(4) (¾x) + (4)y = (4)4
The four cancelled out the fraction….YEAH!!!
3x + 4y = 16
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Let’s Try Some More
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y = ½x – 2
y = 1/3x + 4
y = ¼x – 2
y = 2/5x + 1
Answers:
y = ½x – 2  -x + 2y = -4 or x – 2y = 4
y = 1/3x + 4  -x +3y = 12 or x – 3y = -12
y = -¼x – 2  x + 4y = -8
y = -2/5x + 1  2x + 5y = 5
How Do I Write Standard Form in SlopeIntercept Form?
SOLVE FOR Y!!
 When given 2x + 3y = 9, write in slope-intercept form
 How do I solve for y???
 First get y by itself…..subtract 2x from both sides
 2x + 3y = 9
-2x
-2x
3y = -2x + 9 (You have to write the x first)
3
3
3 (Then divide by 3…EVERYTHING)
 So y = -2/3x + 3
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Let’s Try Some More
Write in Slope-Intercept Form
1.
2x + 4y = 12
2.
-3x + 5y = 10
3.
x – 2y = -6
4.
6x – 4y = 3
Answers:
1.
y = -½x +3
2.
y = 3/5x + 2
3.
y = ½x + 3
4.
y = 3/ x – ¾
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POINT-SLOPE FORM
Linear Equations
What is Point-Slope Form
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It is another way to write a linear equation.
You need a point and the slope (hint: the name)
The formula is
y – y1=m(x – x1)
m= the slope
(x1, y1) is the point.
How do I write an equation in point
slope form?
What is the equation for the line that runs through
(3, 4) and has a slope of -½
 m= -½
 (3 is x1, 4 is y1)
 Put it into the equation!!!
 y- 4 = -½(x – 3)
 And that’s it…..Nothing More!!!
What do you think will be the most common mistake
people will make?.....
Putting the x and y’s in the wrong places!!!
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How can I graph from Point-Slope form?
Graph y – 1 = 1/3 (x – 2)
1st- What is the point?
(2, 1)
2nd – Place the point onto the graph
3rd- What is the slope?
m = 1/3
4th – From the point (2, 1) rise up 1
and go right 3.
5th – Finally, draw a line to connect
the points.