Transcript Linear Equation PowerPoint

LINEAR EQUATIONS PART I
1. Basic Coordinate Plane Info
2. Review on Plotting Points
3. Finding Slopes
4. x and y intercepts
5. Slope-Intercept Form of a Line
6. Graphing Lines
7. Determine the equation of a line given two
points, slope and one point, or a graph.
Objective
• Students will understand how today’s
objective is tied to last week’s learning
COORDINATE PLANE
Y-axis
QUAD II
Parts of a plane
1. X-axis
2. Y-axis
3. Origin
4. Quadrants I-IV
QUAD I
Origin ( 0 , 0 )
X-axis
QUAD III
QUAD IV
PLOTTING POINTS
B
C
D
A
Remember when plotting
points you always start at
the origin. Next you go left
(if x-coordinate is negative)
or right (if x-coordinate is
positive. Then you go up (if
y-coordinate is positive) or
down (if y-coordinate is
negative)
Plot these 4 points
A (3, -4), B (5, 6), C (-4, 5)
and D (-7, -5)
SLOPE
Slope is the ratio of the vertical rise to the horizontal
run between any two points on a line. Usually
referred to as the rise over run. Run is 6
Slope triangle between two
because we points. Notice that the slope
went to the triangle can be drawn two
right
different ways.
Rise is -10
because we
went down
Rise is 10
because we
went up
The slope in this case is
Run is -6
because we
went to the
left
 10 5

6
3
10 5
The slope in this case is

6 3
Another way to
find slope
FORMULA FOR FINDING SLOPE
The formula is used when you know two
points of a line.
They look like A( X1 , Y1 ) and B( X 2 , Y2 )
RISE
Y2  Y1
SLOPE 

RUN X 2  X 1
EXAMPLE
Find the slope of the line between the two points (-4, 8) and (10, -4)
If it helps label the points.
X1 Y1
X2
Y2
Then use the
formula
Y2  Y1
(4)  (8)
X 2  X 1 SUBSTITUTE INTO FORMULA (10)  (4)
Then Simplify 
 12  6

14
7
X AND Y INTERCEPTS
The x-intercept is the x-coordinate of a point
where the graph crosses the x-axis.
The y-intercept is the y-coordinate of a point
where the graph crosses the y-axis.
The x-intercept would be 4 and is
located at the point (4, 0).
The y-intercept is 3 and is
located at the point (0, 3).
SLOPE-INTERCEPT FORM OF A LINE
The slope intercept form of a line is y = mx + b, where
“m” represents the slope of the line and “b”
represents the y-intercept.
When an equation is in slope-intercept form the
“y” is always on one side by itself. It can not be
more than one y either.
If a line is not in slope-intercept form, then we must
solve for “y” to get it there.
Examples
IN SLOPE-INTERCEPT
NOT IN SLOPE-INTERCEPT
y = 3x – 5
y – x = 10
y = -2x + 10
2y – 8 = 6x
y = -.5x – 2
y + 4 = 2x
Put y – x = 10 into slope-intercept form
Add x to both sides and would get y = x + 10
Put 2y – 8 = 6x into slope-intercept form.
Add 8 to both sides then divide by 2 and would get y = 3x + 4
Put y + 4 = 2x into slope-intercept form.
Subtract 4 from both sides and would get y = 2x – 4.
Do you see a pattern??
• What does a linear equation look like?
• Future learning…quadratic, exponential, and
absolute value!
GRAPHING LINES
BY MAKING A TABLE OR USING THE
SLOPE-INTERCEPT FORM
I could refer to the table method by input-output table or x-y table. For now I
want you to include three values in your table. A negative number, zero, and a
positive number.
Graph y = 3x + 2
INPUT (X)
OUTPUT (Y)
-2
-4
0
2
1
5
By making a table it gives me three points, in this case (-2, -4) (0, 2) and (1, 5) to plot
and draw the line.
See the graph.
Plot (-2, -4), (0, 2) and (1, 5)
Then draw the line. Make sure your
line covers the graph and has
arrows on both ends. Be sure to
use a ruler.
Slope-intercept graphing
Slope-intercept graphing
Steps
1. Make sure the equation is in slope-intercept form.
2. Identify the slope and y-intercept.
3. Plot the y-intercept.
4. From the y-intercept use the slope to get another point to draw the line.
1. y = 3x + 2
2. Slope = 3 (note that this means the
fraction or rise over run could be (3/1)
or (-3/-1). The y-intercept is 2.
3. Plot (0, 2)
4. From the y-intercept, we are going
rise 3 and run 1 since the slope was
3/1.
Objective
• Students will be able to write equations
y=mx + b
if given: 1. the slope and y-intercept
2. from a graph
3. the slope and a set of points
4. two sets of points
USE GRAPHIC ORGANIZER!!! For the Obtain
FIND EQUATION OF A LINE GIVEN THE
SLOPE AND Y INTERCEPT
• Slope is -3 and y-intercept is 7
• Slope is ½ and y-intercept is -3
FIND EQUATION OF A LINE GIVEN THE
GRAPH
Ex:
FIND EQUATION OF A LINE GIVEN SLOPE AND
ONE SET OF POINTS
Steps if given the slope and
a point on the line.
1. Substitute the slope into
the slope-intercept
form.
2. Use the point to plug in
for x and y.
3. Find b.
4. Rewrite equation.
If given a graph there are three
ways.
One way is to find two points on
the line and use the first method
we talked about.
Another would be to find the
slope and pick a point and use the
second method.
The third method would be to find
the slope and y-intercept and plug
it directly into y = mx + b.
FIND EQUATION OF A LINE GIVEN SLOPE AND
ONE SET OF POINTS
• Slope 1 point (2,-6)
• Slope ½ point (4,-1)
FIND EQUATION OF A LINE GIVEN 2
POINTS
Find the equation of the line between (2, 5) and (-2, -3).
1. Find the slope between the two
points.
2. Plug in the slope in the slopeintercept form.
3. Pick one of the given points and plug
in numbers for x and y.
4. Solve and find b.
5. Rewrite final form.
1. Slope is 2.
2. y = 2x + b
3. Picked (2, 5) so
(5) = 2(2) + b
4. b = 1
5. y = 2x + 1
Two other ways
FIND EQUATION OF A LINE GIVEN 2
POINTS
• (10,-1) (4,2)
• (-2,-4) (2,-2)
Objective
• Students will be able to write equations
y=mx + b
if given: 1. the slope and y-intercept
2. from a graph
3. the slope and a set of points
4. two sets of points
APPLY NEW LEARNING
• Homework – Kuto Sheet
Extended learning worksheet 5-4 do the odds
Tough problem #22 – Write the equation of a line
that passes through x-intercept 4 and y-intercept -2.